Answer to Question #90721 in Electric Circuits for Christiana

Question

How to calculate current using multiple voltages and parallel and series resistance

Answer 1

All you have to do is to use Kirchhoff's laws. But prior to apply them, you need to draw currents for branches, choose direction as you wish. Also, draw loops and give them directions.

Kirchhoff's current law states that current flowing into the node are positive and current flowing out of the node are negative, and their sum is 0.

Kirchhoff's voltage law states that currents flowing in the directions of loops make positive voltage drops and opposite currents produce negative voltage drops, and their sum is the sum of voltage sources. Voltage sources are positive when drawn in the direction of the loop and vice versa.

Consider an example.

Currents law relatively to the bottom node:

$$I-I_1+I_2=0.$$

Voltage law for the small and the large loops:

$$V_1=I_1Z_1+IZ_4\\0=-IZ_4+I_2Z_2+I_2Z_5.$$

If you know all voltage sources voltages and resistances or impedances (or their equivalents), you'll see that we have three unknown currents and three equations. Solving a system of three equations with three unknowns gives the solution.

Kirchhoff's laws is the simplest method of calculating currents in complex circuits.

Also there are:

Thevenin's theorem;

Norton' s theorem;

Superposition theorem;

Mesh analysis;

Nodal analysis;

and some other rarely used engineering methods of solving that kind of problems.