# Balbharati solutions for Physics 12th Standard HSC Maharashtra State Board chapter 13 - AC Circuits [Latest edition]

## Chapter 13: AC Circuits

Exercises
Exercises [Pages 304 - 305]

### Balbharati solutions for Physics 12th Standard HSC Maharashtra State Board Chapter 13 AC Circuits Exercises [Pages 304 - 305]

Exercises | Q 1.1 | Page 304

Choose the correct option.

If the rms current in a 50 Hz AC circuit is 5A, the value of the current 1/300 seconds after its value becomes zero is ______.

• 5sqrt2 A

• 5sqrt(3/2) A

• 5/6 A

• 5/sqrt2 A

Exercises | Q 1.2 | Page 304

Choose the correct option.

A resistor of 500 Ω and inductance of 0.5 H is in series with an AC source which is given by V = 100 sqrt2 sin (1000 t). The power factor of the combination is ______.

• 1/sqrt2

• 1/sqrt3

• 0.5

• 0.6

Exercises | Q 1.3 | Page 304

Choose the correct option.

In a circuit L, C and R are connected in series with an alternating voltage of frequency f. the current leads the voltage by 45°. The value of C is ______.

• 1/(πf(2πfL - R))

• 1/(2πf(2πfL - R))

• 1/(πf(2πfL + R))

• 1/(2πf(2πfL + R))

Exercises | Q 1.4 | Page 304

Choose the correct option.

In an AC circuit, e and i are given by e = 150 sin(150t)V and i = 150 sin (150t + π/3) A. the power dissipated in the circuit is ______.

• 106W

• 150W

• 5625W

• Zero

Exercises | Q 1.5 | Page 304

Choose the correct option.

In a series LCR circuit, the phase difference between the voltage and the current is 45°. Then the power factor will be ______.

• 0.607

• 0.707

• 0.808

• 1

Exercises | Q 2.1 | Page 304

An electric lamp is connected in series with a capacitor and an AC source is glowing with a certain brightness. How does the brightness of the lamp change on increasing the capacitance?

Exercises | Q 2.2 | Page 304

The total impedance of a circuit decreases when a capacitor is added in series with L and R. Explain why?

Exercises | Q 2.3 | Page 304

For a very high-frequency AC supply, a capacitor behaves like a pure conductor. Why?

Exercises | Q 2.4 | Page 304

What is wattles current?

Exercises | Q 2.5 | Page 304

What is the natural frequency of the LC circuit? What is the reactance of this circuit at this frequency?

Exercises | Q 3 | Page 304

In a series LR circuit XL = R and power factor of the circuit is P1. When capacitor with capacitance C such that XL = XC is put in series, the power factor becomes P2. Calculate P1/P2.

Exercises | Q 4 | Page 304

When an AC source is connected to an ideal inductor show that the average power supplied by the source over a complete cycle is zero.

Exercises | Q 5 | Page 304

Prove that an ideal capacitor in an AC circuit does not dissipate power

Exercises | Q 6 | Page 304

(a) An emf e = e0 sin ωt applied to a series L - C - R circuit derives a current I = I0sinωt in the circuit. Deduce the expression for the average power dissipated in the circuit.
(b) For circuits used for transporting electric power, a low power factor implies large power loss in transmission. Explain.

Exercises | Q 7 | Page 304

A device Y is connected across an AC source of emf e = e0 sin ωt. The current through Y is given as i = i0 sin (ωt + π/2).

1. Identify the device Y and write the expression for its reactance.
2. Draw graphs showing a variation of emf and current with time over one cycle of AC for Y.
3. How does the reactance of the device Y vary with the frequency of the AC? Show graphically.
4. Draw the phasor diagram for device Y.
Exercises | Q 8 | Page 305

Derive an expression for the impedance of an LCR circuit connected to an AC power supply.

Exercises | Q 9 | Page 305

Compare resistance and reactance.

Exercises | Q 10 | Page 305

Show that in an AC circuit containing a pure inductor, the voltage is ahead of current by π/2 in phase.

Exercises | Q 11 | Page 305

An AC source generating a voltage e = e0sinωt is connected to a capacitor of capacitance C. Find the expression for the current i flowing through it. Plot a graph of e and i versus ωt.

Exercises | Q 12 | Page 305

If the effective current in a 50 cycle AC circuit is 5 A, what is the peak value of current? What is the current 1/600 after if was zero?

Exercises | Q 13 | Page 305

A light bulb is rated 100W for 220 V AC supply of 50 Hz. Calculate

1. resistance of the bulb.
2. the rms current through the bulb
Exercises | Q 14 | Page 305

A 15.0 μF capacitor is connected to a 220 V, 50 Hz source. Find the capacitive reactance and the current (rms and peak) in the circuit. If the frequency is doubled, what will happen to the capacitive reactance and the current?

Exercises | Q 15 | Page 305

An AC circuit consists of only an inductor of inductance 2 H. If the current is represented by a sine wave of amplitude 0.25 A and frequency 60 Hz, calculate the effective potential difference across the inductor (π = 3.142)

Exercises | Q 16 | Page 305

Alternating emf of e = 220 sin 100 πt is applied to a circuit containing an inductance of (1/π) henry. Write an equation for instantaneous current through the circuit. What will be the reading of the AC galvanometer connected in the circuit?

Exercises | Q 17 | Page 305

A 25 μF capacitor, a 0.10 H inductor, and a 25Ω resistor are connected in series with an AC source whose emf is given by e = 310 sin 314 t (volt). What is the frequency, reactance, impedance, current, and phase angle of the circuit?

Exercises | Q 18 | Page 305

A capacitor of 100 μF, a coil of resistance 50Ω, and an inductance 0.5 H are connected in series with a 110 V-50Hz source. Calculate the rms value of current in the circuit.

Exercises | Q 19 | Page 305

Find the capacity of a capacitor which when put in series with a 10Ω resistor makes the power factor equal to 0.5. Assume an 80V-100Hz AC supply.

Exercises | Q 20 | Page 305

Find the time required for a 50 Hz alternating current to change its value from zero to the rms value.

Exercises | Q 21 | Page 305

Calculate the value of the capacity in picofarad, which will make 101.4 microhenry inductance to oscillate with a frequency of one megahertz.

Exercises | Q 22 | Page 305

A 10 μF capacitor is charged to a 25 volt of potential. The battery is disconnected and a pure 100 m H coil is connected across the capacitor so that LC oscillations are set up. Calculate the maximum current in the coil.

Exercises | Q 23 | Page 305

A 100 μF capacitor is charged with a 50 V source supply. Then source supply is removed and the capacitor is connected across an inductance, as a result of which 5A current flows through the inductance. Calculate the value of the inductance.

Exercises

## Balbharati solutions for Physics 12th Standard HSC Maharashtra State Board chapter 13 - AC Circuits

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Concepts covered in Physics 12th Standard HSC Maharashtra State Board chapter 13 AC Circuits are AC Circuits, AC Generator, Average and RMS Values, Phasors, Different Types of AC Circuits, Power in Ac Circuit, LC Oscillations, Electric Resonance, Sharpness of Resonance: Q Factor, Choke Coil.

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