Calculate the total energy developed in 5 minutes by the system above.

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The circuit diagram contains an inconsistency: if the two $40 \, \Omega$ resistors are in parallel, their equivalent resistance is $20 \, \Omega$ . If the total current is $1.2 \, \text{A}$ , the voltage across them would be $V = I \times R = 1.2 \, \text{A} \times 20 \, \Omega = 24 \, \text{V}$ , which contradicts the $12 \, \text{V}$ shown by the voltmeter. To find a matching answer from the options, we will assume the total current ( $1.2 \, \text{A}$ ) and the resistor values ( $40 \, \Omega$ ) are correct, and the $12 \, \text{V}$ reading is a distractor.

Calculate the equivalent resistance of the two parallel resistors.
For two resistors in parallel, the equivalent resistance $R_{eq}$ is given by:
$\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2}$ $\frac{1}{R_{eq}} = \frac{1}{40 \, \Omega} + \frac{1}{40 \, \Omega}$ $\frac{1}{R_{eq}} = \frac{2}{40 \, \Omega}$ $R_{eq} = \frac{40 \, \Omega}{2} = 20 \, \Omega$
Calculate the total power developed by the system.
The total current $I$ is $1.2 \, \text{A}$ . The power $P$ is given by $P = I^2 R_{eq}$ .
$P = (1.2 \, \text{A})^2 \times 20 \, \Omega$ $P = 1.44 \, \text{A}^2 \times 20 \, \Omega$ $P = 28.8 \, \text{W}$
Convert the time from minutes to seconds.
The time $t$ is $5 \, \text{minutes}$ .
$t = 5 \, \text{minutes} \times 60 \, \frac{\text{s}}{\text{minute}}$ $t = 300 \, \text{s}$
Calculate the total energy developed.
The energy $E$ is given by $E = P \times t$ .
$E = 28.8 \, \text{W} \times 300 \, \text{s}$ $E = 8640 \, \text{J}$
The calculated energy matches option E.

The final answer is $\text{E } 8640 \text{ J}$ .

Calculate the total energy developed in 5 minutes by the system above.

Answer

Step-by-step solution

Calculate the equivalent resistance of the two parallel resistors.

Calculate the total power developed by the system.

Convert the time from minutes to seconds.

Calculate the total energy developed.

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