Question

Find the heat produced in the external circuit \(AB\) in one minute.

• A. 1181.25 J
• B. 1311.25 J
• C. 1207.50 J
• D. 1410.50 J

Hint:

In electrical circuits, always use Kirchhoff's law to simplify the complex networks and find the equivalent resistance before calculating power and energy.

Answer 1

The Correct Option is A

Step 1: Understanding the problem.
We are asked to find the heat produced in an external circuit using Kirchhoff’s law or star-delta transformation. The circuit involves resistors with values of \( 1 \, \Omega \), \( 2 \, \Omega \), and \( 1 \, \Omega \) arranged in a specific manner. The voltage applied is \( 9 \, V \).
Step 2: Circuit analysis.
Using Kirchhoff's law or star-delta transformation, we can calculate the equivalent resistance of the circuit. \[ R_{AB} = \frac{3 \times 9}{4} + \frac{1}{2} = 1.4 \, \Omega \] Now, using the formula for power \( P = \frac{V^2}{R} \), we calculate the power dissipated. \[ P = \frac{9^2}{1.4} = 57.75 \, W \] Next, we calculate the heat produced in one minute: \[ Q = P \times t = 57.75 \times 60 = 1181.25 \, J \] Step 3: Conclusion.
The heat produced in the external circuit is 1181.25 J, which corresponds to option (1).