Topic: Network Theory
A resistor and a capacitor are connected in series with a sine wave generator having frequency such that the resistance and the capacitive reactance are same i.e. voltage across capacitance, $V_{C}$ is equal to Voltage across Resistance, $V_{R}$. If the frequency of the sine wave generator is doubled, then
- A. $V_{R}<V_{C}$
- B. $V_{R}=V_{C}$
- C. $V_{R}>V_{C}$
- D. None of the above
Answer: C. $V_{R}>V_{C}$
Explanation: Initially, $V_R = V_C$, which means $R = X_C = \frac{1}{2\pi f C}$.
If the frequency $f$ is doubled, the capacitive reactance $X_C$ halves, while the resistance $R$ remains the same. Since the same current flows through both, $V_R = I \times R$ and $V_C = I \times X_{C_{new}}$. Because $R > X_{C_{new}}$, it follows that $V_R > V_C$.