Physics Ninja: Mastering Ohm's Law and DC Circuits

Review how charge is quantized with the elementary charge of 1.6e-19 C, and how electrons move under F = qE and a = F/m in a battery-driven field.

Current equals the flow of moving charges. With charge density n, cross section A, and drift velocity v, the current is I = n e A v.

Explore the definition of current as the rate of charge flow, measured in amperes, and relate it to charge density, electron density, cross-sectional area, and drift velocity in a wire.

Explore how copper's conduction arises from delocalized electrons, whose motion is randomized by collisions and thermal fluctuations yet yields a net drift under an electric field, about 1 mm/s.

learn the convention that positive current flows opposite to electron flow, with current direction defined opposite to electrons' drift velocity and consistent with the electric field direction.

Learn how current density J relates to total current I in a constant-density cross section, where I = J times area and units are amps per square meter.

Compute the drift velocity and total charge of free electrons in one meter of copper wire from density, radius, and Avogadro's number, yielding about 3.6×10^-5 m/s and 2.8×10^4 C.

Estimate the 1-meter electron drift time from battery to starter motor using drift velocity, showing about 7.5 hours.

Explore resistance and Ohm's law, linking electric field and current density to voltage, with R = ρL/A and the effects of length and area on current in conductors.

Examine the units in Ohm's law, including current (amps), current density (amps per meter squared), electric field (volts per meter), and resistivity (ohm-meters), plus conductivity as its reciprocal.

Demonstrates Ohm's law by showing that voltage is proportional to current through resistance and that resistance depends on resistivity, length, and cross-sectional area.

Identify how ohmic resistors show a linear voltage–current relationship with constant resistance, and explain non-ohmic devices where resistance varies with voltage and current.

Explore ohm's law relation R = rho L / A, resistivity differences among copper, silver, and rubber, and how temperature increases resistivity and resistance.

Master resistor color codes to determine resistance in ohms, covering four-, five-, and six-band resistors, including digits, multipliers, tolerance, and which side to start reading.

Learn to read four-band color codes to calculate resistance, identify digits and a multiplier, and apply 10% tolerance to a 15,000-ohm resistor.

Explore the American wire gauge system, showing how wire diameter and cross section affect copper wire resistance and current capacity, with practical notes from Home Depot examples.

Compute the resistance of a 3-meter 14-gauge copper wire using R = ρL/A, with ρ ≈ 1.7×10⁻⁸ Ω·m and diameter about 1.6 mm to get R about 0.025 Ω.

Explore energy and electric circuits, examining power from batteries, resistance dissipation, and electromotive forces, with a focus on steady state currents and closed loops per ohm's law.

Understand electromotive force as the work per unit charge that a battery does to move electrons, driving current in a loop, and relate emf to current via Ohm's law.

Explore how internal resistance lowers terminal voltage and current in a circuit by applying Ohm's law to a battery with emf E, a resistor, and neglecting wire resistance.

Explain how a battery's internal resistance lowers terminal voltage as current increases, using emf minus i r, with a 12 volt battery and 0.5 ohms example.

Explain how power arises from moving charge between higher and lower potentials, define current and voltage, and derive power as IV and I²R using Ohm's law.

Explore what a kilowatt hour (kWh) represents as total energy, and how to convert it to joules. Understand how electricity cost depends on energy used, about 12 cents per kWh.

Learn symbols for voltage sources (parallel lines, long positive, short negative; E or V), resistors (sawtooth), wires (no resistance), and switches (open or closed) and how open circuits stop current.

Identify whether resistors are in series or parallel to simplify electric circuits, then apply Ohm's law to compute power in those configurations.

Resistors in series carry the same current through each resistor, while voltage drops add up. Ohm's law links these drops to total resistance, which equals the sum of the resistors.

Explore resistors in parallel, derive the equivalent resistance, and apply ohm's law and current conservation at junctions to show 1/r_eq = 1/r1 + 1/r2.

Master the two-resistor parallel trick: find the equivalent resistance as r_eq = (r1 * r2) / (r1 + r2) by multiplying and then dividing by the sum, with simple examples.

Extend parallel resistance to three resistors by summing reciprocals to get 1/r_eq = 1/r1 + 1/r2 + 1/r3, yielding r_eq = 2/3 ohm for the example.

Simplify a seven-resistor network with a 5-volt supply by identifying series and parallel paths to obtain a 10-ohm equivalent, then apply Ohm's law to find 0.5 A.

Explore solving mixed series and parallel resistor networks by finding the equivalent resistances: case one yields 5/3 ohms, case two yields 2.4 ohms.

Learn to find the equivalent resistance of a complex resistor network by reshaping the circuit, identifying series and parallel groups, and simplifying step by step.

Learn why simple series and parallel reductions sometimes fail to find equivalent resistance, identify when circuits can’t be simplified, and preview alternative methods for circuits with multiple power supplies.

Apply Kirchhoff's rules to solve complete circuit problems, whether single or multi-loop, and compute currents in every resistor, voltmeter readings, and power dissipation using Ohm's law.

Explore Kirchoff's current law, the junction rule, where currents entering a junction equal currents leaving, reflecting conservation of charge with a clear sign convention.

Apply Kirchhoff's current law to multiple junctions (a through e) to determine currents and directions, solving for unknowns by balancing currents entering and leaving each node.

Apply current law at junctions to find i3 in the outermost branch of a three-resistor circuit: 7 A entering and 2.5 A and 1.5 A leaving, i3 equals 3 A.

Master Kirchoff's voltage loop rule: the sum of potential differences around a closed circuit loop equals zero. See how crossing batteries and resistors and loop direction influence the results.

Apply Kirchhoff's loop rule to dc circuits by selecting loops and current directions, then compute battery gains and resistor drops using Ohm's law.

Practice applying Kirchhoff's loop rule to analyze voltage drops and gains around different circuits, set up loop equations, and solve for unknown currents using Ohm's law.

Explore Kirchhoff's voltage law on a single loop circuit with a battery and two resistors, using potential differences and Ohm's law to analyze voltage drops.

Solve single loop circuits by computing current, voltage differences between points, and power delivered and dissipated using ohm's law and kirchoff's voltage law.

Analyze a single-loop circuit with two opposite-polarity power supplies and a 1 A current. Learn energy balance as stronger source charges the weaker battery while dissipating 5 W as heat.

Learn to solve multi-loop dc circuits by assigning branch currents, simplifying with an equivalent resistance, and applying Kirchhoff's junction and loop rules to determine battery and branch currents.

Solve currents in a multiloop circuit by forming an equivalent resistance from parallel branches and applying ohm's law, then use loop and junction rules for branch currents.

Examine how picking the wrong current direction affects junction and loop rules, yet yields 4.3-ohm equivalent resistance and a 2.3 ampere current, with a negative result signaling to switch direction.

Demonstrates how Kirchoff's voltage law governs parallel circuits, showing identical branch voltages, current distribution according to resistance, and relationships such as i3 equals i1/2 in a 12-volt network.

Analyze a multi-loop circuit, apply Ohm's law and series-parallel reduction to find currents, voltages, and the power dissipated by the five-ohm resistor.

Explore the voltage divider: two resistors in series split source voltage via Ohm's law and Kirchhoff's loop rule, letting you drive other circuits at a lower voltage.

Analyze a real battery with internal resistance in series with a load to illustrate impedance matching, showing maximum power when the load equals the internal resistance.

Explore how ammeters measure current by placing them in series with low resistance, and how voltmeters measure voltage in parallel with high resistance to avoid circuit disruption.

Balance in a Wheatstone bridge yields zero center current, so the unknown resistor X equals (R2×R3)/R1, as shown with R1=15, R2=900, R3=50 giving 3000 ohms.

Introduction to rc circuits shows how capacitors introduce time-dependent currents and voltages, explains charging versus discharging, and covers capacitor symbols, capacitance in farads, and q(t) linked to voltage.

Close the switch in an rc circuit to observe a transient current that charges the capacitor, with current decaying as the capacitor voltage rises toward the emf.

Explore the RC circuit's long-time behavior: the current tends to zero, the capacitor voltage equals the battery emf, and the final charge QF equals C times emf, independent of resistance.

Derive the capacitor charging current i(t) in an RC circuit using calculus and Kirchhoff's voltage law, yielding q(t)=C E (1−e^{−t/RC}) and i(t)=(E/R) e^{−t/RC}.

Explore how a capacitor charges in an RC circuit, deriving charge and voltage and defining the RC time constant tau, while noting how R and C affect charging speed.

Compute the current as a function of time for charging a capacitor, starting with the battery emf over the resistance and decaying exponentially with the RC time constant.

Close the switch to discharge the capacitor and apply Kirchhoff’s loop rule to derive Q(t)=Q0 e^{-t/(RC)}, V(t)=Q0/C e^{-t/(RC)}, and i(t) decays as e^{-t/(RC)}.

Analyze charging and discharging RC circuits, showing how capacitor energy evolves over time and can be written as 1/2 C V^2 or 1/2 Q^2/C, with time-dependent power and exponential behavior.

Analyze complex RC circuits by examining short time and long time limits, where the capacitor acts as a short circuit initially and as an open circuit later, using Kirchhoff's laws.

Practice 30 multiple choice problems on resistors and capacitors to test your understanding of ohm's law and dc circuits. Watch paired videos for solutions and review the answer key.

Apply ohm's law to two questions: compute the bulb's resistance as 240 ohms from 120 volts and 60 watts; identify the unit as ohms, i.e., volts per ampere.

Two copper wires with different lengths and cross sections reveal resistivity stays constant, so resistivity ratio is one; rewrite Ohm's law to relate current density and electric field to resistivity.

Analyze how drift velocity scales with current and cross-sectional area in two tungsten wires, yielding a drift velocity ratio of two, and discuss metals' resistivity increasing linearly with temperature.

Apply ohm's law to determine voltmeter readings across a circuit with a battery's internal resistance. Problem 7 yields 10 volts; problem 8 yields 7 volts depending on meter orientation.

Compute the electron count from a 2-ampere current over 2 seconds, yielding about 2.5×10^19 electrons, and analyze an 18-ohm resistor for power at 3 volt and 1 volt.

Analyze five circuits on a single battery to determine which has the least current, linking highest equivalent resistance to the result, and smallest resistance to greatest power.

Problem 13 shows the internal resistance is 0.4 ohms from (6 − 5.8)/0.5. For problem 14, to raise power dissipated, decrease the wire’s resistance by reducing length and resistivity.

Apply loop-rule analysis to series and parallel resistors to determine internal resistance, yielding r = 1 ohm for the series case and r = 4 ohms for the parallel case.

Identify the current as an inverse function of resistance using Ohm's law, and explain that in a parallel pair with R1 much larger than R2, the equivalent resistance is about R2.

Explore three identical resistors in series and parallel to identify the equivalent resistance, and apply P=I^2R to show that tripling resistance triples power under the same current.

Apply Ohm's law to dc circuits by analyzing brightness changes as a switch opens and closes, then compute total resistance and current in mixed series and parallel networks.

Apply ohm's law to find four volts across the 2-ohm resistor in problem 23. Determine the current through the 6-ohm resistor via junction and parallel rules, yielding about 10.7 watts.

Explore short-time and long-time behavior in dc circuits: the current is maximal after switch closure, while the capacitor charge rises toward a maximum as current eventually vanishes.

Analyze a simple dc circuit with a 9-volt battery and 40.5-ohm resistance to compute power and energy, and determine the rc time constant in a series circuit.

Demonstrates ammeter in series and voltmeter in parallel for measuring current and voltage, and derives power dissipation in a battery with internal resistance and a light bulb via total resistance.

Practice Kirchhoff's rules and current calculations in dc circuits with resistors and batteries through a 16-problem set, covering single-branch and multi-loop circuits and power dissipation or delivery.

Analyze a series circuit of 4 ohm and 6 ohm resistors with a 12-volt battery; compute 10 ohm equivalent, 1.2 A, 4.8 V and 7.2 V drops, and 14.4 W.

Analyze a 12 volt parallel circuit with 4 ohm and 6 ohm resistors. Find the equivalent resistance of 2.4 ohms and the branch currents using Ohm's law.

Identify series and parallel resistors; show 1 and 6 are in series, 3 and 4 are in parallel, then simplify by combining 3 and 4 in parallel and proceed.

Master how to simplify complex resistor networks by identifying parallel and series sections to find the total equivalent resistance, illustrated by deriving a 6-ohm network.

explain series and parallel resistor combinations, derive total resistance as six ohms, find a 3 amp current from an 18-volt source, and assess switch effects.

Learn to find potentials in a single-loop series circuit using equivalent resistance, determine a 0.5 A current, and analyze energy transfer between 12 V and 4 V batteries.

Apply Kirchhoff's rules to a multi-loop circuit, write junction and loop equations to solve for branch currents, then compute the power in the 4-ohm resistor and energy.

Apply ohm's law to a 12-volt circuit with 3, 4, and 6 ohm resistors, obtaining currents 4 A, 3 A, and 2 A, then 9/2 ohms and 8/3 A total.

Apply Kirchhoff's loop and junction rules to a three-branch multiloop circuit with three batteries and three resistors, solving for each branch current. Note that equivalent-resistance simplifications fail here due to the batteries.

Compute the power delivered to resistors in a 20-volt DC circuit with four resistors. Use Ohm's law, current division, and series-parallel reductions to find power dissipated.

Compute currents and voltages in a three-branch circuit by applying junction rules, simplifying parallel resistors to an equivalent, and solving loop equations.

Relate powers in a three-resistor circuit by simplifying parallel R2 and R3 into R1, then find current from emf and compute P for R1, R2, and R3.

Combine series and parallel resistors to find the equivalent resistance, then apply ohm's law to compute total current and branch currents, using junction rules for current division.

Master Ohm's law in dc circuits by calculating the equivalent resistance using series and parallel combinations, then apply junction and loop rules to solve branch currents.

Determine the unknown resistance in a dc circuit by analyzing open and closed switch configurations, applying loop and junction rules, and using currents in the main and branch paths.

Use junction and loop rules to solve a multi-branch dc circuit with three batteries and three resistors, find currents, and calculate resistor power and battery power.

Practice solving RC circuit problems by calculating time constants, voltages at different times, and plate charge, then review the eight or nine problems in the PDAF document with solutions.

Discharge a capacitor in a 1 kΩ, 2 μF RC circuit using Q(t)=Q0 e^{-t/RC} to find the time for 99% discharge, about 9.2×10^-3 s.

Apply the discharge formula Q(t)=Q0 e^{-t/RC} to a capacitor in a simple resistor-capacitor circuit, calculating remaining charge after five milliseconds as about 1.21 microcoulombs.

In this RC charging example, a 12-volt battery powers a 10 MΩ resistor and 1 μF capacitor. At 46 seconds the charge is about 99% of the final charge.

Apply Kirchhoff's loop rule to the circuit; after a long time the capacitor is fully charged, no current flows in that branch, and the capacitor voltage equals the 10-volt battery.

Solve a long-time dc circuit: show the center branch carries no current, reduce to a single loop of three resistors, compute current, then find the capacitor voltage near 7 V.

Determine the initial current at time zero in a resistor-capacitor network by shorting capacitors, comparing parallel paths, and computing the equivalent resistance for a quick Ohm's law result.

Calculate the energy dissipated in the fifty five hundred ohm resistor during the one-second discharge. Observe initial energy of 0.25 joules at 50 volts and final energy about 0.04 joules.

At t=0 the capacitor shorts, giving 3 A through the 4 Ω branch and 0 through the 8 Ω branch; at steady state it opens and charges to 48 μC.

Analyze an rc circuit to determine resistance from a 50-volt source and a 2 μf capacitor, using voltages across capacitor and resistor at 4 seconds.