Question

In the circuit shown below, the magnitude of the voltage \( V_1 \) in volts across the 8 kΩ resistor is ________. (round off to nearest integer)

Hint:

Use Kirchhoff's Voltage Law (KVL) to solve for voltages and currents in a circuit with resistors in series or parallel.

Answer 1

Correct Answer: 98

Using Kirchhoff’s Voltage Law (KVL) in the circuit, the sum of the voltages around the loop should be zero. Given that \( V_1 \) is the voltage across the 8 kΩ resistor and the current \( I \) flows through both the 2 kΩ resistor and the 8 kΩ resistor, we can write the KVL equation: \[ 75 = 2I + 0.5V_1 + V_1 \] The total current \( I \) is: \[ I = \frac{75}{2k + 8k} = \frac{75}{10k} = 7.5 \, \text{mA} \] Now substitute the value of \( I \) into the equation: \[ 75 = 2(7.5 \, \text{mA}) + 0.5V_1 + V_1 \] Simplifying: \[ 75 = 15 + 0.5V_1 + V_1 \] \[ 75 - 15 = 1.5V_1 \] \[ 60 = 1.5V_1 \] Solving for \( V_1 \): \[ V_1 = \frac{60}{1.5} = 40 \, \text{V} \] Thus, the magnitude of the voltage \( V_1 \) across the 8 kΩ resistor is \( \boxed{40} \) V.