# H C VERMA Solutions for Class 12-science Physics Chapter 17 - Alternating Current

## Chapter 17 - Alternating Current Exercise 330

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

Equation of alternating current

After time t, it reaches rms value

ms

The household supply of electricity is at 220V (rms value) and 50Hz. Find the peak voltage and the least possible time in which the voltage can change from the rms value to zero.

Peak voltage,

Volt

Equation of alternating voltage

Time taken from rms value to zero is equal to time taken from zero to rms value.

ms

A bulb rated 60W at 220V is connected across a household supply of alternating voltage of 220V. Calculate the maximum instantaneous current through the filament.

Resistance of the bulb

Now,

An electric bulb is designed to operate at 12 volts DC. If this bulb is connected to an AC source and gives normal brightness, what would be the peak voltage of the source?

Since, brightness is same. So, heat consumed in DC and AC will be same.

volt

The peak power consumed by a resistive coil when connected to an AC source is 80W. Find the energy consumed by the coil in 100 seconds which is many times larger than the time period of the source.

RMS value of power

Energy consumed

The dielectric strength of air is 3.0×
10^{6} V/m. A parallel-plate air-capacitor has area 20cm^{2 }and
plate separation 0.10mm. Find the maximum rms voltage of an AC source which
can be safely connected to this capacitor.

V/m

Potential difference across the capacitor

volt

Rms value of voltage which can be connected

volt

The current in the discharging LR circuit is given by where Ʈ is the time constant of the circuit. Calculate the rms current for the period t=0 to t= Ʈ.

A capacitor of capacitance 10µF is connected to an oscillator giving an output voltage. Find the peak currents in the circuit for.

Capacitive reactance,

Peak voltage, V_{0 }= 10
Volt

(a) At

(b) At

(c) At

(d) At

A coil of inductance 5.0mH and negligible resistance is connected to the oscillator of the previous problem. Find the peak currents in the circuit for

Inductive reactance,

Peak voltage, V_{0
}= 10 Volt

Now,

(a)

(b)

(c)

A coil has a resistance of 10Ω and an inductance of 0.4 henry. It is connected to an Ac source of 6.5V, Hz. Find the average power consumed in the circuit.

Impedance of the circuit

Power consumed=

W

A resistor of resistance 100Ω is connected to an AC source. Find the energy dissipated as heat during t=0 to t=0.1ms.

Energy dissipated as heat

J

In a series RC circuit with an AC source, R=300Ω,
C=25μF,
ε_{0}=
50v and v = 50/π Hz. Find the peak current and the average power
dissipated in the circuit.

Hz

Impedance of the circuit

Peak current

A

Average power dissipated

W

An electric bulb is designed to consume 55W when operated at 110 volts. It is connected to a 220V, 50Hz line through a choke coil in series. What should be the coil for which the bulb gets correct voltage?

Resistance of the bulb

Potential drop across resistance volt

Potential drop
across inductor V_{L}

Applied potentialvolt

I=0.5A

So, current through inductor is I=0.5A

Now, for inductor

H

In a series LCR circuit with an AC source, R=300Ω, C=20μF, L=1.0henry, V and v = 50/π Hz. Find (a) the rms current in the circuit. (b) The rms potential differences across the capacitor, the resistor and the inductor. Note that the sum of the rms potential differences across the three elements is greater than the rms voltage of the source.

Hz

R=300

Impedance

(a) Rms current in the circuit

A

(b) volt

volt

volt

Consider the situation of the previous problem. Find the average electric field energy stored in the capacitor and the average magnetic field energy stored in the coil.

Energy stored in the capacitor

mJ

Energy stored in the Inductor

mJ

An inductance of 2.0H, a capacitance of 18μF and a resistance of 10kΩ are connected to an Ac source of 20V with adjustable frequency. (a) What frequency should be chosen to maximize the current in the circuit? (b) What is the value of this maximum current?

(a) Current is maximum when circuit is in resonance condition

Hz

(b) Impedance

Z=R=10kΩ

Now,

V=IZ

I=2mA

An inductor-coil, a capacitor and an AC source of rms voltage 24V are connected in series. When the frequency of the source is varied, a maximum rms current of 6.0A is observed. If this inductor coil is connected to a battery of emf 12V and the internal resistance 4.0Ω, what will be the current?

Impedance of the circuit is equal to resistance of circuit as current is maximum when impedance is minimum.

V=IZ

24=6.Z

Z=4Ω

Now, when battery is connected,

Current in circuit

V=IR

12=I (8)

I=1.5A

Figure shows a typical circuit for low pass filter. An AC
input v_{i} = 10mV is applied at the left end and the output v_{0}
is received at the right end. Find the output voltages for and. Note that as the frequency is increased the output
decreases and hence the name low pass filter.

Impedance of the circuit

Current in the circuit

Potential drop across capacitor

(a) f=10kHz

mV

(b) f=100kHz

mV

(c) f=kHz

mV

(d) f=kHz

V

A transformer has 50 turns in the primary and 100 in the secondary. If the primary is connected to 220V DC supply, what will be the voltage across the secondary?

Zero voltage across secondary coil as there is no change in flux.

### Kindly Sign up for a personalised experience

- Ask Study Doubts
- Sample Papers
- Past Year Papers
- Textbook Solutions

#### Sign Up

#### Verify mobile number

Enter the OTP sent to your number

Change