Q21GATE 2003MCQ

A reading of 120 is obtained when standard inductor was connected in the circuit of a Q-meter and the variable capacitor is adjusted to value of 300 pF. A lossless capacitor of unknown value $C_{x}$ is then connected in parallel with the variable capacitor and the same reading was obtained when the variable capacitor is readjusted to a value of 200 pF. The value of $C_{x}$ in pF is

🚀 Solve in Practice Mode

📖 Explanation

\begin{aligned} \text{Q of the coil}&= 120\\ Q&= \frac{\omega L}{R}=\frac{1}{\omega RC} \end{aligned}

CASE-I: Q=120 is obtained for C=300pF CASE-II: For the same reading i.e. Q=120 Effective capacitance of the circuit shuold be 300 pF. Effective capacitance of parallel capacitor

\begin{aligned} C_{eff}&= C+C_x\\ C_x&= C_{eff}-C\\ &= 300-200\\ &= 100pF \end{aligned}

Q22GATE 2002MCQ

Two in-phase, 50 Hz sinusoidal waveform of unit amplitude are fed into channel 1 and channel 2 respectively of an oscilloscope. Assuming that the voltage scale, time scale and other settings are exactly the same for both the channels, what would be observed if the oscilloscope is operated in X-Y mode?

🚀 Solve in Practice Mode

📖 Explanation

$\therefore \;\; \text{Phase difference}=0^{\circ} \text{also} f_x=f_y.$