If $\mathrm { R } _ { 1 } = 12 \mathrm { k } \Omega$ and $\mathrm { R } _ { 2 } = 5\mathrm { k } \Omega$ and they are wired in series across a 20 V source, what is VR₁ and VR₂ ? A) $\mathrm { VR } 1 = 0 \mathrm {~V} , \mathrm { VR } 2 = 20 \mathrm {~V}$ B) $\mathrm { VR } 1 = 5.88 \mathrm {~V} , \mathrm { VR } 2 = 14.12 \mathrm {~V}$ C) $\mathrm { VR } 1 = 10 \mathrm {~V} , \mathrm { VR } 2 = 10 \mathrm {~V}$ D) $\mathrm { VR } 1 = 14.12 \mathrm {~V} , \mathrm {~V} R 2 = 5.88 \mathrm {~V}$

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Quizplus · Accepted Answer

In a series circuit, the voltage is divided among the resistors in proportion to their resistances. The total resistance is $ R_1 + R_2 = 17 \mathrm{k}\Omega $. The current $ I = \frac{20V}{17k\Omega} \approx 1.176 \mathrm{mA} $. Thus, $ VR_1 = I \times R_1 = 1.176 \mathrm{mA} \times 12k\Omega = 14.12V $ and $ VR_2 = I \times R_2 = 1.176 \mathrm{mA} \times 5k\Omega = 5.88V $.

If R1=12kΩ\mathrm { R } _ { 1 } = 12 \mathrm { k } \OmegaR1​=12kΩ

If $\mathrm { R } _ { 1 } = 12 \mathrm { k } \Omega$