Basic Concepts of Electrical Circuits

Explain Ohm's law, where current is proportional to the potential difference under constant conditions, yielding v over i equals r, v equals i r, and i equals v over r.

Learn the series connection of resistors, where the same current flows through R1, R2, and R3, voltages add, and the equivalent resistance equals the sum of the resistances.

Explore series resistors by calculating the equivalent resistance and current using Ohm's law, illustrated with 5 ohms, 3 ohms, and 2 ohms in a 10-volt circuit.

Explore the parallel resistor network across a source voltage. Apply Ohm's law to find i1, i2, i3 and derive 1/r_eq = 1/r1 + 1/r2 + 1/r3, extend to n resistors.

Examine a parallel network of 4, 6, and 12 ohms across 12 volts, compute the equivalent resistance as 2 ohms, and obtain a 6-ampere current via Ohm's law.

Combine two series and three parallel resistors to compute total resistance, then apply Ohm's law to find current and the voltage across a 2 ohm resistor.

Apply the current divider rule to determine i1 and i2 in a parallel circuit, using r1 and r2 with v, with i1 = I r2/(r1+r2) and i2 = I r1/(r1+r2).

Use current divider rules on a 12-volt parallel circuit of 3 ohm and 6 ohm resistors, compute equivalent resistance, total current, and branch currents I1 and I2 with Ohm's law.

Learners determine the equivalent resistance of a circuit by series and parallel combinations. The example yields 8 ohms between terminals A and B.

Kirchhoff's current law states that the algebraic sum of currents at a junction is zero, with incoming currents positive and outgoing currents negative.

Apply Kirchhoff’s voltage law to a closed circuit by summing emf and voltage drops to zero, using sign conventions for rises and falls in potential.

Apply KCL and KVL to a four-branch circuit to determine branch currents. The result shows AB, BC, CD currents and DA zero, with I = -20 A.

Apply Kirchhoff’s current and voltage laws to a circuit with multiple registers, solve for I1 and I2, and determine currents through the 4 Ω, 3 Ω, and 6 Ω resistors.

Apply Kirchhoff’s voltage law to determine currents in loops and drops across 2 ohm and 3 ohm resistors, then find the potential difference between B and H as 1 volt.

Apply Maxwell's mesh current method by dividing a circuit into non-splitting meshes, assigning mesh currents, and using Kirchhoff's voltage law to solve for mesh currents, then derive branch currents.

Divide the network into two meshes, assign currents I1 and I2, apply Kirchhoff's voltage law, and find the current in branch BE as the algebraic sum of I1 and I2.

Apply the mesh current method and Kirchhoff's voltage law to three loops to determine I1, I2, and I3, with BG = I1−I2 and CF = I2−I3.

Apply nodal analysis to solve a network using Kirchhoff’s current law, designate a reference node and independent nodes, assign branch currents, solve for node voltages, and determine branch currents.

Apply nodal analysis and Kirchhoff’s current law to a three-node network; solve for VB and VC, then compute branch currents I3 and I5 in BE and CE.

Apply the superposition theorem to circuits with multiple sources by replacing all but one source with their internal resistance and summing the algebraic currents from each source.

Apply superposition theorem to determine currents through resistors in a circuit with sources, internal resistances, and open-circuit conditions, and compute the equivalent resistance in series and parallel branches.