Exams › JEE Advanced › Physics

A lamp rated 50 W, 100 V is connected in series with a capacitor of capacitance 50/(pi*sqrt(x)) microfarad across a 200 V, 50 Hz AC supply. The lamp glows at its rated value. Determine the value of x.

1. 1
2. 2
3. 3
4. 4

Correct answer: 3

Solution

Rated current of the lamp I = P/V = 50/100 = 0.5 A. Lamp resistance behaves as a resistor; its voltage drop is 100 V (in phase with current). The capacitor voltage V_C is 90 deg out of phase. Source: 200² = 100² + V_C², so V_C = sqrt(40000 - 10000) = sqrt(30000) = 100*sqrt(3) V. Reactance X_C = V_C/I = 100*sqrt(3)/0.5 = 200*sqrt(3) ohm. Since X_C = 1/(2*pi*f*C), C = 1/(2*pi*50*200*sqrt(3)) = 1/(20000*pi*sqrt(3)) F = (50/(pi*sqrt(3))) microfarad. Comparing with 50/(pi*sqrt(x)) gives x = 3.

Related JEE Advanced Physics questions

• A resistor and an ideal inductor are connected in series in an AC circuit. Three ideal hot-wire voltmeters V1, V2, and V3 are connected across the resistor, the inductor, and the AC source respectively. Which relation correctly describes the readings?
• In an AC circuit, the power factor changes from 1/2 to 1/4 while the resistance remains unchanged. By what percentage should the impedance be increased to achieve this change in power factor?
• In an LC oscillating circuit, at a certain instant the charge on the capacitor is Q and the current through the inductor is I. At this instant the energy stored in the capacitor equals the energy stored in the inductor. What is the time period of the electrical oscillations?
• An AC source with emf V = V0*(sin(wt) + sin(3wt)) is connected in series with a capacitor C and a resistor R. The resulting current is expressed as i = i1*sin(wt + phi1) + i2*sin(3wt + phi2). Which of the following correctly compares i1 and i2?
• A series LCR circuit having a resistance of 100 ohm is driven by an AC source of 400 V (rms) at an angular frequency of 300 rad/s. When the capacitor is disconnected from the circuit, the current lags behind the applied voltage by 60 degrees. When the inductor is disconnected instead, the current leads the applied voltage by 60 degrees. Find the rms current and the power dissipated in the complete LCR circuit.
• A capacitor with reactance X_C = 10 ohm and an inductor with reactance X_L = 5 ohm are connected in parallel across an AC voltage source V = 100 V. Find the ratio of the current through the inductor to the total current drawn from the source.

⚔️ Practice JEE Advanced Physics free + battle 1v1 →