QuestionMay 3, 2025

2 Data: V=12V R1=1Omega R2=1Omega R3=1Omega R4=1Omega R5=0.05Omega What is the total power consumed by the glow plugs? square w OK

2 Data: V=12V R1=1Omega R2=1Omega R3=1Omega R4=1Omega R5=0.05Omega What is the total power consumed by the glow plugs? square w OK
2 Data: V=12V R1=1Omega R2=1Omega R3=1Omega R4=1Omega R5=0.05Omega What is the total power consumed by the glow plugs? square w OK

Solution
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Answer

1.72W Explanation 1. Calculate equivalent resistance of the circuit R_3, R_4, and R_5 are in parallel. Use **\frac{1}{R_{eq}} = \frac{1}{R_3} + \frac{1}{R_4} + \frac{1}{R_5}**: \frac{1}{R_{eq}} = \frac{1}{1} + \frac{1}{1} + \frac{1}{0.05} = 1 + 1 + 20 = 22 R_{eq} = \frac{1}{22} \approx 0.0455\Omega 2. Combine series resistances Add R_1, R_2, and R_{eq} (series connection): R_{total} = R_1 + R_2 + R_{eq} = 1 + 1 + 0.0455 = 2.0455\Omega 3. Calculate total current Use **I = \frac{V}{R_{total}}**: I = \frac{12}{2.0455} \approx 5.87A 4. Calculate power consumed by glow plugs (R_5) Use **P = I^2R** for R_5: P = (5.87)^2 \cdot 0.05 \approx 1.72W

Explanation

1. Calculate equivalent resistance of the circuit<br /> $R_3$, $R_4$, and $R_5$ are in parallel. Use **$\frac{1}{R_{eq}} = \frac{1}{R_3} + \frac{1}{R_4} + \frac{1}{R_5}$**:<br />$\frac{1}{R_{eq}} = \frac{1}{1} + \frac{1}{1} + \frac{1}{0.05} = 1 + 1 + 20 = 22$<br />$R_{eq} = \frac{1}{22} \approx 0.0455\Omega$<br /><br />2. Combine series resistances<br /> Add $R_1$, $R_2$, and $R_{eq}$ (series connection): <br />$R_{total} = R_1 + R_2 + R_{eq} = 1 + 1 + 0.0455 = 2.0455\Omega$<br /><br />3. Calculate total current<br /> Use **$I = \frac{V}{R_{total}}$**:<br />$I = \frac{12}{2.0455} \approx 5.87A$<br /><br />4. Calculate power consumed by glow plugs ($R_5$)<br /> Use **$P = I^2R$** for $R_5$: <br />$P = (5.87)^2 \cdot 0.05 \approx 1.72W$
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