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

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Chapter 17 - Alternating Current Exercise 330

Question 1

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

Solution 1

Equation of alternating current

  

After time t, it reaches rms value   

  

  

  

 ms

Question 2

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.

Solution 2

  

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

Question 3

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.

Solution 3

Resistance of the bulb

  

Now,

  

  

  

  

Question 4

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?

Solution 4

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

  

  

  

  

 volt 

Question 5

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.

Solution 5

RMS value of power

  

  

Energy consumed

   

  

Question 6

The dielectric strength of air is 3.0× 106 V/m. A parallel-plate air-capacitor has area 20cm2 and plate separation 0.10mm. Find the maximum rms voltage of an AC source which can be safely connected to this capacitor.

Solution 6

  

  

 V/m

Potential difference across the capacitor

  

 volt

Rms value of voltage which can be connected

 volt

Question 7

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. 

Solution 7

  

   

  

  

  

  

  

Question 8

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

Solution 8

Capacitive reactance,   

Peak voltage, V0 = 10 Volt

  

  

  

(a) At   

   

 

(b) At   

   

 

(c) At   

   

 

(d) At   

   

Question 9

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   

Solution 9

Inductive reactance,   

Peak voltage, V0 = 10 Volt

Now,

  

  

(a)   

  

(b)   

   

(c)   

  

Question 10

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.

Solution 10

Impedance of the circuit

  

  

  

 Power consumed=  

  

  

 W

Question 11

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

Solution 11

Energy dissipated as heat

  

  

  

  

  

  

  

 J

Question 12

In a series RC circuit with an AC source, R=300Ω, C=25μF, ε0= 50v and v = 50/π Hz. Find the peak current and the average power dissipated in the circuit.

Solution 12

 Hz

Impedance of the circuit

  

  

  

Peak current

  

 A

Average power dissipated

  

  

 W 

Question 13

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?

Solution 13

Resistance of the bulb

  

 

 

Potential drop across resistance  volt

Potential drop across inductor VL

Applied potential volt

  

  

I=0.5A

So, current through inductor is I=0.5A

Now, for inductor

  

  

  

  

  

 H

Question 14

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. 

Solution 14

 Hz

  

  

R=300  

Impedance   

  

 

(a) Rms current in the circuit

  

  

  A

 

(b)  volt

 volt 

 volt  

Question 15

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.

Solution 15

Energy stored in the capacitor

  

 mJ

Energy stored in the Inductor

  

 mJ

Question 16

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?

Solution 16

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

  

  

  

 Hz

 

(b) Impedance

Z=R=10kΩ 

Now,

V=IZ

  

I=2mA

Question 17

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?

Solution 17

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

Question 18

Figure shows a typical circuit for low pass filter. An AC input vi = 10mV is applied at the left end and the output v0 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.

 

  

 

Solution 18

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

Question 19

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?

Solution 19

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