Alternating Current — Class 12 Physics PYQs

The alternating current I in an inductor is observed to vary with time t as shown in the graph for a cycle.
Which one of the following graphs is the correct representation of wave form of voltage V with time t ?
(A) [Graph]
(B) [Graph]
(C) [Graph]
(D) [Graph]

A voltage $v=v_0\sin \omega t$ applied to a circuit drives a current $i=i_0\sin (\omega t+\varphi )$ in the circuit. The average power consumed in the circuit over a cycle is
(A) Zero
(B) $i_0{v}_0\cos \varphi$
(C) $\frac{i_0{v}_0}{2}$
(D) $\frac{i_0{v}_0}{2}\cos \varphi$

The ratio of the number of turns of the primary to the secondary coils in an ideal transformer is 20 : 1. If 240 V ac is applied from a source to the primary coil of transformer and a 6.0 $\Omega$ resistor is connected across the output terminals, then current drawn by the transformer from the source will be -
(A) 4.0 A
(B) 3.8 A
(C) 0.97 A
(D) 0.10 A

A transformer is connected to a 200 V ac source. The transformer supplies 3000 V to a device. If the number of turns in the primary coil is 450, then the number of turns in its secondary coil is –
(A) 30
(B) 450
(C) 4500
(D) 6750

Assertion (A) : In an ideal step-down transformer, the electrical energy is not lost.
Reason (R) : In a step-down transformer, voltage decreases but the current increases.

Differentiate between the peak value and root mean square value of an alternating current. Derive the expression for the root mean square value of alternating current, in terms of its peak value.

ac voltage of frequency $\omega$ is applied across a series LCR circuit. Draw the phasor diagram and obtain the impedance of the circuit.
(b) Discuss 'resonance' in a series LCR circuit and write the expression for resonant frequency.

Which of the following quantity/quantities remains same in primary and secondary coils of an ideal transformer ?
Current, Voltage, Power, Magnetic flux
(A) Current only
(B) Voltage only
(C) Power only
(D) Magnetic flux and Power both

A resistor and an ideal inductor are connected in series to a 100$\sqrt{2}$ V, 50 Hz ac source. When a voltmeter is connected across the resistor or the inductor, it shows the same reading. The reading of the voltmeter is :
(A) 100$\sqrt{2}$ V
(B) 100 V
(C) 50$\sqrt{2}$ V
(D) 50 V

A series LCR circuit (L = 2 mH, C = 0.2 $\mu$F and R = 30 $\Omega$) is connected to an ac source of variable frequency. The impedance of this circuit will be minimum at a frequency of :
(A) $\frac{10^5}{4\pi }$ Hz
(B) $\frac{10^5}{2\pi }$ Hz
(C) $\frac{10^4}{4\pi }$ Hz
(D) $\frac{10^4}{2\pi }$ Hz