Free-Ed: Basic Electronics Fundamentals

Basic Circuit Analysis
Parallel Circuits

Section 2-3 Kirchhoff's Current Law

Important Fact

The voltage in a parallel circuit is the same across component and equal to the source voltage.

V_T = V₁ = V₂ = V₃ = ... = V_n

Circuit 1

Circuit 2

This is an example of a very general type of parallel circuit�not just a battery and three resistors connected in series. We don't know exactly what the Source is. It might be a battery, an electrical generator, or any other source of electrical energy. Likewise the loads aren't necessarily resistors. They might be lamps, electronic equipment, or any other appliance that presents a fixed resistive load.

The important point is that the Source is providing 24V. This is a parallel circuit, so you can be confident that the source is providing 24V to each of the loads.

Important Facts

The sum of currents through each resistor in a parallel circuit is equal to the total total.

I_T = I₁ + I₂ +I₃ + ... + I_n

The source voltage in this example is 24V. You can see that the same 24-volt level appears across all the resistors that are connected in parallel with it.

The source current happens to be 70mA. That is also the circuit's total current. The important thing to see here is that the branch currents add up to the source, or total, current.

Finding the Total Current of a Parallel Resistor Circuit

Example

Here is a simple 2-resistor parallel circuit. Let:

V_T = 24V

R₁ = 100W

R₂ = 300W

Given those values for total voltage and each resistor:

Determine the total resistance -- R_T
Determine the total current -- I_T
Determine the voltage across each resistor -- V_R1, V_R2
Determine the current through each resistor -- I_R1, I_R2

When solving parallel resistor circuits, you are most often given the voltage of the source (V_T) and the value of each resistor.

Given that information, you can use the equations for parallel resistance to calculate the total resistance (R_T) of the circuit.

Knowing the total voltage and resistance, you can use Ohm's Law to find the total current: IT = VT/RT

Procedure

Given the source voltage (VT) and values of all

Find the total resistance (RT)

Calculate the total current IT = VT/RT