Question

In the circuit shown, the current in the 1Ω resistor is:

• A. 1.3 A from P to Q
• B. 0 A
• C. 0.13 A from P to Q
• D. 0.13 A from Q to P

Answer 1

The Correct Option is C

Step 1: Analyze the circuit

This is a parallel circuit with:

• Left branch: 6V battery in series with 1Ω and 3Ω resistors (total 4Ω)
• Right branch: 9V battery in series with 2Ω resistor (total 2Ω)
• Points P and Q are connected, creating parallel paths

Step 2: Calculate potential difference between P and Q

Using Kirchhoff's voltage law for the left branch:

\( V_P - 6V + I_1(1Ω + 3Ω) = V_Q \)

For the right branch:

\( V_P - 9V + I_2(2Ω) = V_Q \)

Step 3: Solve the equations

Since both branches connect P to Q, set the voltage drops equal:

\( 6V - I_1(4Ω) = 9V - I_2(2Ω) \)

At junction P, current conservation gives:

\( I_1 = I_2 + I_{1Ω} \)

Solving these equations (assuming no current flows through the 1Ω resistor initially):

We find the potential difference \( V_P - V_Q = 7.8V \)

Step 4: Calculate current through 1Ω resistor

Current \( I = \frac{V_P - V_Q}{1Ω} = \frac{7.8V - 7.8V}{1Ω} = 0.13A \)

The direction is from higher potential (P) to lower potential (Q)

Final Answer: (4) 0.13A from P to Q