Question 32

The Correct Answer is A ### Explanation of the Correct Answer (A) The power consumed by a resistor ($P$) is calculated using the formula $P = I^2 R$, where $I$ is the current flowing through the resistor and $R$ is the resistance value. Figure B illustrates a series circuit where the total applied voltage ($V_{total}$) is 24 V, and the resistors $R_1$, $R_2$, and $R_3$ are connected end-to-end. **1. Calculate the Total Resistance ($R_{total}$):** In a series circuit, the total resistance is the sum of individual resistances: $R_{total} = R_1 + R_2 + R_3$ $R_{total} = 3 \, \Omega + 4 \, \Omega + 5 \, \Omega = 12 \, \Omega$ **2. Calculate the Total Current ($I_{total}$):** The current is the same throughout a series circuit. Use Ohm's Law ($I = V/R$): $I_{total} = V_{total} / R_{total}$ $I_{total} = 24 \, \text{V} / 12 \, \Omega = 2 \, \text{A}$ Since the circuit is in series, the current flowing through $R_2$ ($I_{R2}$) is the total current: $I_{R2} = 2 \, \text{A}$ **3. Calculate the Power Consumed by $R_2$ ($P_{R2}$):** Use the power formula $P = I^2 R$: $P_{R2} = (I_{R2})^2 \times R_2$ $P_{R2} = (2 \, \text{A})^2 \times 4 \, \Omega$ $P_{R2} = 4 \, \text{A}^2 \times 4 \, \Omega = 16 \, \text{W}$ Therefore, the power consumed by $R_2$ is 16 watts. --- ### Explanation of Incorrect Options **B) 20 watts:** This value does not correspond to the power dissipation of $R_2$. For comparison, the power dissipated by $R_3$ (5 $\Omega$) is $P_{R3} = (2 \text{ A})^2 \times 5 \, \Omega = 20 \, \text{W}$. This option represents the power consumed by R3, not R2. **C) 24 watts:** This value is likely derived from an error such as calculating the power of $R_1$ and $R_2$ combined ($R_1 + R_2 = 7 \, \Omega$) if the current was incorrectly assumed (e.g., $I=2$ A, $P = 4 \times 7 = 28$ W - which is Option D), or perhaps an attempt to calculate the voltage drop across $R_2$ (8V) multiplied by a mistakenly calculated current (3 A, which is incorrect). It does not match the actual power of $R_2$ (16 W). **D) 28 watts:** This value is the power consumed by the first two resistors combined ($P_{R1} + P_{R2}$): $P_{R1} = (2 \, \text{A})^2 \times 3 \, \Omega = 12 \, \text{W}$ $P_{R1} + P_{R2} = 12 \, \text{W} + 16 \, \text{W} = 28 \, \text{W}$. This option represents the combined power of R1 and R2, not the power consumed by R2 alone.