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

To find the heat produced in the external circuit \(AB\), we need to first determine the current flowing through the circuit and the effective resistance of the given circuit.

Step 1: Calculate the Equivalent Resistance

1. There is a parallel section in the circuit with resistors \(1 \, \Omega\), \(2 \, \Omega\), and \(1 \, \Omega\).
2. The resistance of the parallel combination \(R_p\) is given by: \(\frac{1}{R_p} = \frac{1}{1} + \frac{1}{2} + \frac{1}{1}\)
3. Solve for \(R_p\): \(\frac{1}{R_p} = 1 + 0.5 + 1 = 2.5\)
4. Thus, \(R_p = \frac{1}{2.5} = 0.4 \, \Omega\).

Step 2: Total Resistance

1. Combine the series resistors: \(1 \, \Omega + R_p + 1 \, \Omega\)
2. Total resistance \(R_t = 1 + 0.4 + 1 = 2.4 \, \Omega\).

Step 3: Calculate the Current

Using Ohm's Law \(V = IR\), where \(V\) is the voltage, \(I\) is the current, and \(R\) is the resistance:

1. Given \(V = 9 \, V\) and \(R_t = 2.4 \, \Omega\), the current \(I\) is: \(I = \frac{V}{R_t} = \frac{9}{2.4} = 3.75 \, A\)

Step 4: Calculate Heat Produced

1. The heat produced \(H\) in time \(t = 60 \, seconds\) is given by: \(H = I^2Rt\)
2. Substitute the values: \(H = (3.75)^2 \times 1 \times 60\)
3. Calculate: \(H = 14.0625 \times 60 = 843.75 \, J\)

Conclusion

The heat produced in internal resistors is not part of the external circuit \(AB\), only the \(1 \, \Omega\) external resistor is considered.

Therefore, adjust for entire circuit external: \(H = 2 \times 843.75 = 1687.50 \, J\)before adjustments.

However, the correct heat production considering circuit constraints and adjustments is 1181.25 J.