Alternating Current

Previous Years' CBSE Board Questions

7.1 Introduction

MCQ

1. The figure shows variation of current (I) with time (t) in four devices P, Q, R and S. The device in which an alternating current flows is
2. Plot a graph showing variation of capacitive reactance with the change in the frequency of the ac source. (AI 2015C)

SAI (2 marks)

An ac source of emf <math>V = V_0 \sin \omega t</math> is connected to a

capacitor of capacitance C. Deduce the expression

for the current (I) flowing in it. Plot the graph of

(i) V vs ωt, and (ii) I vs ωt. (2020) OR Show that the current leads the voltage in phase by

<math>\pi/2</math> in an ac circuit containing an ideal capacitor.

(Foreign 2014) S

SAII SA II (3 marks)

The figure shows the graphical variation of the

reactance of a capacitor with frequency of ac source.

1. P (b) Q (c) R (d) S

(2023)

7.2 AC Voltage Applied to a Resistor

MCQ

14 Reactance (Ω) 12 8 10 6- 2 The rms current in a circuit connected to a 50 Hz ac source is 15 A. The value of the current in the circuit <math>\left(\frac{1}{600}\right)</math>s after the instant the current is zero, is

1. <math>\frac{15}{\sqrt{2}}</math> A (b) 15√2 A
2. <math>\frac{\sqrt{2}}{15}</math> A (d) 8 A (Term I 2021-22)

2 0 100 200 300 400

Frequency (Hz)

7.5 AC Voltage Applied to a Capacitor MCQ

1. An ac voltage <math>v = v_0 \sin \omega t</math> is applied to a series combination of a resistor R and an element
2. The instantaneous current in the circuit is <math>I = I_0 \sin\left(\omega t + \frac{\pi}{A}\right)</math>. Then which of the following is correct?

1. X is a capacitor and X_C = √2R
2. X is an inductor and <math>X_L = R</math>
3. X is an inductor and <math>X_L = \sqrt{2}R</math>

(2023)

1. X is a capacitor and <math>X_C = R</math>

VSA (1 mark)

1. What is the impedance of a capacitor of capacitance C in an ac circuit using source of frequency n Hz?

(2020) R

1. Define capacitive reactance. Write its S.I. units. (Delhi 2015) [II]

(2018)

1. A device 'X' is connected to an ac source <math>V = V_0 \sin \omega t</math>. The variation of voltage, current and power in one cycle is shown in the following graph:

Y 4 В → ωt∙ <math>2\pi</math>

1. Identify the device 'X'.
2. Which of the curves A, B and C represent the voltage, current and the power consumed in

reactance of a capacitor with frequency of ac source.

1. Find the capacitance of the capacitor.
2. An ideal inductor has the same reactance at 100 Hz frequency as the capacitor has at the same frequency. Find the value of inductance of the inductor.
3. Draw the graph showing the variation of the reactance of this inductor with frequency.

(2020) (Ap)

(5 marks)

1. A device X is connected across an ac source of voltage <math>V = V_0 \sin \omega t</math>. The current through X is given as <math>l = l_0 \sin \left( \omega t + \frac{\pi}{2} \right)</math>
2. Identify the device X and write the expression for its reactance.
3. Draw graphs showing variation of voltage and current with time over one cycle of ac, for X.
4. How does the reactance of the device X vary with frequency of the ac? Show this variation graphically.
5. Draw the phasor diagram for the device X.

The voltage across a resistor, an inductor, and a

capacitor connected in series to an ac source are

20 V, 15 V and 30 V respectively. The resultant

voltage in the circuit is

1. 5 V (b) 20 V (c) 25 V (d) 65 V (Term I 2021-22)

A circuit is connected to an ac source of variable

frequency. As the frequency of the source is

increased, the current first increases and then

decreases. Which of the following combinations of

elements is likely to comprise the circuit?

1. L, C and R (b) Land C
2. L and R (d) R and C (Term I 2021-22)