Question

An L-R-C series circuit has voltage amplitudes VL = 180 V, Vc = 120 V, and VR = 160 V. At time t the instantaneous voltage across the inductor is 80.0 V.

Part A At this instant, what is the voltage across the capacitor? Express your answer with the appropriate units. vc = | Value Units

Part B At this instant, what is the voltage across the resistor? Express your answer with the appropriate units. ? T: MÅ VR= Value 0 0 Units

Answer 1

The voltage across the capacitor in an L-R-C series circuit is the same as the voltage across the inductor, which in this case is 80.0 V. The voltage across the resistor can be calculated by subtracting the voltage across the inductor and the capacitor from the total voltage in the circuit, resulting in 20 V.

Step-by-step explanation:

In an L-R-C series circuit, the voltage across the inductor leads the current by one-fourth of a cycle, the voltage across the capacitor follows the current by one-fourth of a cycle, and the voltage across the resistor is in phase with the current. Since the voltage across the inductor is given as 80.0 V, we can deduce that the voltage across the capacitor is also 80.0 V and is in phase with the voltage across the inductor. Therefore, the voltage across the capacitor is 80.0 V.

The voltage across the resistor can be calculated by subtracting the voltage across the inductor and the voltage across the capacitor from the total voltage in the circuit. The total voltage is given as 180 V, and the voltage across the inductor and capacitor is 80 V each. Therefore, the voltage across the resistor is 180 V - 80 V - 80 V = 20 V.

Answer 2

The voltage across the capacitor at the instant when the inductor voltage is 80 V is 40 V because the capacitor and inductor voltages are 180° out of phase. The voltage across the resistor does not change instantaneously as it is in phase with the current and is thus 160 V.

Step-by-step explanation:

In an L-R-C series circuit, the instantaneous voltages across the inductor (VL), capacitor (Vc), and resistor (VR) are related due to Kirchhoff's voltage law, which states that the sum of the potential differences (voltage) around any closed network is zero. Given that the instantaneous voltage across the inductor is 80 V, and the voltage amplitudes are VL = 180 V, Vc = 120 V, and VR = 160 V, voltages across the capacitor and resistor can be calculated by making use of the fact that the voltages across the inductor and the capacitor are 180° out of phase.

Part A: At the instant when the voltage across the inductor VL is 80 V, the voltage across the capacitor Vc will be the amplitude Vc = 120 V minus the instantaneous voltage across the inductor since they are 180° out of phase. Therefore, the voltage across the capacitor at this instant is Vc = 40 V.

Part B: As the voltage across the resistor VR is in phase with the current, the instantaneous voltage across it remains the same as its amplitude, which is VR = 160 V.