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: Circuit Analysis

The circuit is parallel, comprising:

• Left branch: A 6V battery in series with resistors totaling 4Ω (1Ω + 3Ω).
• Right branch: A 9V battery in series with a 2Ω resistor (total 2Ω).
• Points P and Q are interconnected, establishing parallel paths.

Step 2: Potential Difference Calculation (P to Q)

Applying Kirchhoff's voltage law to the left branch:

\( V_P - 6V + I_1(1Ω + 3Ω) = V_Q \)

Applying Kirchhoff's voltage law to the right branch:

\( V_P - 9V + I_2(2Ω) = V_Q \)

Step 3: Equation Solving

Equating the voltage drops between P and Q for both branches:

\( 6V - I_1(4Ω) = 9V - I_2(2Ω) \)

Current conservation at junction P:

\( I_1 = I_2 + I_{1Ω} \)

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

The potential difference is determined to be \( V_P - V_Q = 7.8V \)

Step 4: Current Through 1Ω Resistor Calculation

The current through the 1Ω resistor is calculated as:

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

The current flows from the higher potential (P) to the lower potential (Q).

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