Find the current through 8 Ω resistor, in the following circuit:

Concept

Any voltage or current in a complex electrical circuit can be found by using Thevenin Theorem.

Thevenin Theorem:

Thevenin’s theorem states that it is possible to simplify any linear circuit, into an equivalent circuit with a single voltage source and a series resistance.

Steps to calculate:

1. Thevenin Resistance (Rth): Open the circuit to the terminal from where the Thevenin resistance has to be found. While finding the Rth, short circuit the independent voltage source and open circuit the independent current source.
2. Thevenin Voltage (Vth): This is the open-circuit voltage across the terminals where the load was connected.

Calculation

Step 1: Calculation of Thevenin Voltage

V₁ = 10 × 9 = 90 V

\(V_2=45\times{6\over 6+3}=30\space V\)

\(V_{th}=V_1-V_2\)

\(V_{th}=90-30=60\space V\)

Step2: Calculation of Thevenin Resistance

6Ω and 3Ω are in parallel.

\(R={6\times 3\over 6+3}=2Ω\)

R_th = 12Ω 

The current across 8Ω is given by:

\(I={60\over 12+8}=3\space A\)