Chapter 37, Problem 1PLA

50639-37-1PLA                                                                                        AID: 1825 | 11/04/2020

To determine

The relationship between the generator voltage, the capacitor voltage and the resistor voltage.

Answer to Problem 1PLA

Option (c) $V_C$ lags $V_R$ by $90°$, $V$ lags $V_R$ by angle $\varphi$.

Explanation of Solution

For a series circuit with a capacitor, resistor and a generator, its corresponding voltages form a right triangle.

In $RC$ circuit the voltage across resistance and the capacitors are out of phase at an angle is $90°$ and the resistor’s voltage leads the capacitor’s voltage.

Conclusion:

1. (a) From figure, the generator voltage $V$ and the resistor’s voltage $V_R$ are out of phase. Thus, option (a) is incorrect.
2. (b) From figure, the generator voltage $V$ leads the capacitor’s voltage $V_C$ by angle $\varphi$. Thus, option (b) is incorrect.
3. (c) From figure, the capacitor’s voltage $V_C$ lags the resistor’s voltage $V_R$ by $90°$, the generator voltage $V$ lags the resistor’s voltage $V_R$ by angle $\varphi$. Thus, option (c) is correct.
4. (d) From figure, the generator voltage $V$ leads the capacitor’s voltage $V_C$ by angle $\varphi$. Thus, option (d) is incorrect