A 22 $\mathrm { k } \Omega$ and 12 $\mathrm { k } \Omega$
resistor are connected across a 68 V source. How is the voltage divided?
A) 34 V and 34 V
B) 22 V and 12 V
C) 44 V and 24 V
D) 68 V and 68 V

Question

A 22 $\mathrm { k } \Omega$ and 12 $\mathrm { k } \Omega$
 resistor are connected across a  68 V  source. How is the voltage divided?
A)  34 V and  34 V
B)  22 V  and  12 V
C)  44 V  and  24 V
D)  68 V  and  68 V

Quizplus · Accepted Answer

The voltage division rule states that the voltage across a resistor in a series circuit is given by $V = V_{\text{total}} \times \frac{R}{R_{\text{total}}}$, where $V_{\text{total}}$ is the total voltage across the circuit, $R$ is the resistance of the resistor in question, and $R_{\text{total}}$ is the total resistance of the circuit. Here, $R_{\text{total}} = 22 \, \mathrm{k\Omega} + 12 \, \mathrm{k\Omega} = 34 \, \mathrm{k\Omega}$. For the 22 $\mathrm{k\Omega}$ resistor, $V = 68 \, \mathrm{V} \times \frac{22 \, \mathrm{k\Omega}}{34 \, \mathrm{k\Omega}} = 44 \, \mathrm{V}$, and for the 12 $\mathrm{k\Omega}$ resistor, $V = 68 \, \mathrm{V} \times \frac{12 \, \mathrm{k\Omega}}{34 \, \mathrm{k\Omega}} = 24 \, \mathrm{V}$.

A 22 kΩ\mathrm { k } \OmegakΩ And 12 kΩ\mathrm { k } \OmegakΩ

A 22 $\mathrm { k } \Omega$ And 12 $\mathrm { k } \Omega$