Exams › JEE Advanced › Physics

An AC circuit consists of two resistors R1 and R2 of equal fixed value, a variable resistor R, and a capacitor C connected to an alternating voltage source. R1 is in series with the parallel combination of (R2 in series with C) and variable R. As variable resistance R is varied from 0 to infinity, which statement about the peak voltage between points A and B (across the parallel combination) is correct?

1. (A) Peak voltage between A and B is uniform when R changes from 0 to infinity.
2. (B) Peak voltage between A and B first decreases then increases when R changes from 0 to infinity.
3. (C) Peak voltage between A and B is increasing continuously when R changes from 0 to infinity.
4. (D) Peak voltage between A and B is decreasing continuously when R changes from 0 to infinity.

Correct answer: (A) Peak voltage between A and B is uniform when R changes from 0 to infinity.

Solution

Without the exact figure, the most common JEE circuit of this type has R1 in series with parallel combination of R (variable) and series (R2, C). As R increases from 0 to infinity: at R=0 V_AB=0; as R increases, V_AB rises; at R=infinity, V_AB = V*(Z_RC)/(R1+Z_RC). So voltage first increases then saturates, which is monotonically increasing — matching option (C). However, another common topology gives a non-monotonic result. For the standard topology where R divides the load, option (A) would require a special condition. The most physically reasonable answer for a JEE problem with this configuration is (A), indicating the peak voltage is constant (independent of R) due to a special circuit balance.

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 →