Physics Part I Chapter 7 Alternating Current

The teachers of Geeta’s school took the students on a study trip to a power generating station, located nearly 200 km away from the city. The teacher explained that electrical energy is transmitted over such a long distance to their city, in the form of alternating current (ac) raised to a high voltage. At the receiving end in the city, the voltage is reduced to operate the devices. As a result, the power loss is reduced. Geeta listened to the teacher and asked questions about how the ac is converted to a higher or lower voltage.

1. Name the device used to change the alternating voltage to a higher or lower value. State one cause for
   power dissipation in this device.
2. Explain with an example, how power loss is reduced if the energy is transmitted over long distances as an alternating current rather than a direct current.
3. Write two values each shown by the teachers and Geeta.

A device X is connected across an ac source of voltage V=V₀sin ωt. The current through X is given as $\mathrm{I} - {\mathrm{I}}_0\sin \left(\mathrm{\omega t} + \frac{\mathrm{\pi }}{2}\right)$

1. Identify the device X and write the expression for its reactance.
2. Draw graphs showing a variation of voltage and current with time over one cycle ac, for X.
3. How does the reactance of the device X vary with the frequency of the ac? Show this variation graphically.
4. Draw the phasor diagram for the device X.

In an a.c. circuit the voltage applied is E = E₀ sinπt. The resulting current in the circuit is I = I₀ sin .The power consumption in the circuit is given by

• 

• P = zero

• 
• 

A current I flows along the length of an infinitely long, straight, thin walled pipe. Then 

• the magnetic field is zero only on the axis of the pipe

• the magnetic field is different at different points inside the pipe

• the magnetic field at any point inside the pipe is zero

• the magnetic field at all points inside the pipe is the same, but not zero

In a series resonant LCR circuit, the voltage across R is 100 volts and R = 1 kΩ with C = 2µF. The resonant frequency ω is 200 rad/s. At resonance the voltage across L is

• 4 × 10−3 V

• 2.5 × 10⁻² V

• 40 V

• 250 V

Two voltameters one of copper and another of silver, are joined in parallel. When a total charge q flows through the voltameters, equal amount of metals are deposited. If the electrochemical equivalents of copper and silver are z₁ and z₂ respectively the charge which flows through the silver voltameter is

A circuit has a resistance of 12 Ω and an impedance of 15 Ω. The power factor of the circuit will be

• 0.8

• 0.4

• 1.25

• 0.125

The phase difference between the alternating current and emf is π/2. Which of the following cannot be the constituent of the circuit?

• C alone

• R.L

• L.C

• L alone

Alternating current can not be measured by D.C. ammeter because

• A.C. cannot pass through D.C.

• A.C. changes direction

• average value of current for complete cycle is zero

• D.C. ammeter will get damaged.

In an LCR series a.c. circuit, the voltage across each of the components, L, C and R is 50 V. The voltage across the LC combination will be

• 50 V

• 50√2 V

• 100 V

• 0 V(zero)

In a LCR circuit capacitance is changed from C to 2C. For the resonant frequency to remain unchanged, the inductance should be changed from L to

• 4L

• 2L

• L/2

• L/4

For an RLC circuit driven with a voltage of amplitude v_m and frequency ${\omega }_0 = \frac{1}{\sqrt{LC}}$ the current exhibits resonance. The quality factor, Q is given by:

• $\frac{CR}{{\omega }_0}$

• $\frac{{\omega }_{0}L}{R}$

• $\frac{{\omega }_{0}R}{L}$

• $\frac{R}{\left({\omega }_{0}C\right)}$

An EM wave from air enters a medium. The electric fields are

${\overrightarrow{E}}_1 = E_{01} \hat{x} \cos \left[2\pi v\left(\frac{z}{c}-t\right)\right]$ in air and ${\overrightarrow{E}}_2 = E_{02} \hat{x} \cos [ k(2z-ct\left)\right]$ in medium, where the wave number k and frequency v refer to their values in air. The medium is non-magnetic. If ${\epsilon }_{r_1} and {\epsilon }_{r_2}$refer to relative permittivities of air and medium respectively, which of the following options is correct ?

• $\frac{{\epsilon }_{r_1}}{{\epsilon }_{r_2}} = \frac{1}{2}$

• $\frac{{\epsilon }_{r_1}}{{\epsilon }_{r_2}} = 4$

• $\frac{{\epsilon }_{r_1}}{{\epsilon }_{r_2}} = 2$

• $\frac{{\epsilon }_{r_1}}{{\epsilon }_{r_2}} = \frac{1}{4}$

In an electromagnetic wave in free space the root mean square value of the electric field is E rms= 6 V/m. The peak value of the magnetic field is

• 1.41 × 10–⁸ T

• 2.83 × 10^–8 T

• 0.70 × 10^–8 T

• 4.23 × 10^–8 T

An inductor 20 mH, a capacitor 100 µF and a resistor 50 Ω are connected in series across a source of emf, V = 10 sin 314 t. The power loss in the circuit is

• 0.79 W

• 0.43

• 1.13

• 2.74 W

An L.C. circuit is in the state of resonance. If C = 0.1F and L = 0.25 Henry. Neglecting ohmic resistance of circuit. What is the frequency of oscillations?

• 1007 Hz

• 100 Hz

• 100 Hz

• 500 Hz

When temperature of an ideal gas is increased from 27°C to 227°C, its rms speed is changed from 400 m/s to v_s Then, v_s is

• 516 m/s

• 450 m/s

• 310 m/s

• 746 m/s

In a L-C-R circuit, the capacitance is made one-fourth, then what should be changed in inductance, so that the circuit remains in resonance?

• 8 IMES

• 1/4 times

• 2 times

• 4 times

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

• $\frac{1}{2\mathrm{\pi f} \left(2\mathrm{\pi f} \mathrm{L} + \mathrm{R}\right)}$

• $\frac{1}{\mathrm{\pi f} \left(2\mathrm{\pi f} \mathrm{L} + \mathrm{R}\right)}$

• $\frac{1}{2\mathrm{\pi f} \left(2\mathrm{\pi f} \mathrm{L} - \mathrm{R}\right)}$

• $\frac{1}{\mathrm{\pi f} \left(2\mathrm{\pi f} \mathrm{L} - \mathrm{R}\right)}$

In a series L-C-R circuit, resistance R = 10 Ω and the impedance Z = 10 Ω. The phase difference between the current and the voltage is

• 0^o

• 30^o

• 45^o

• 60^o

The impedance of a circuit, when a resistance R and an inductor of inductance L are connected in series in an AC circuit of frequency f, is

• $\sqrt{\mathrm{R} + 2 {\mathrm{\pi }}^2 {\mathrm{f}}^2 {\mathrm{L}}^2}$

• $\sqrt{\mathrm{R} + 4{\mathrm{\pi }}^2 {\mathrm{f}}^2 {\mathrm{L}}^2}$

• $\sqrt{{\mathrm{R}}^2 + 4 {\mathrm{\pi }}^2 {\mathrm{f}}^2 {\mathrm{L}}^2}$

• $\sqrt{{\mathrm{R}}^2 + 2{\mathrm{\pi }}^2 {\mathrm{f}}^2 {\mathrm{L}}^2}$

A choke is preferred to a resistance for limiting current in AC circuit because

• choke is cheap

• there is no wastage of power

• choke is compact in size

• choke is a good absorber of heat

Induced emf in the coil depends upon

• conductivity of coil

• amount of flux

• rate of change of linked flux

• resistance of coil

In an L-C-R circuit inductance is changed from L to L/2.To keep the same resonance frequency, C should be changed to

• 2 C

• $\frac{\mathrm{C}}{2}$

• 4 C

• $\frac{\mathrm{C}}{4}$

220 V, 50 Hz, AC source is connected to an inductance of 0.2 Hand a resistance of 20 Ω in series. Whatis the current in the circuit?

• 3.33 A

• 33.3 A

• 5 A

• 10 A

If we change the value of R, then

• voltage does not change on L

• voltage does not change on LC combination

• voltage does not change on C

• voltage changes on LC combination

Real power consumption in a circuit is least when it contains.

• high R, low L

• high R, high L

• low R, high L

• high R, low C

The rms speed (in m/s) of oxygen molecules of the gas at temperature 300 K, is

• 483

• 504

• 377

• 346

An inductor (L = 20 H), a resistor (R = 100 Ω) and a battery (E = 10 V) are connected in series. After a long time, the circuit is short-circuited and then the battery is disconnected. Find the current in the circuit at 1 ms after short circuiting.

• 4.5 x 10⁵ A

• 3.2x 10^-5 A

• 9.8 × 10^-5 A

• 6.7 × 10^-4 A

The magnetic flux through each turn of a coil having 200 turns is given as (t² $-$ 1) x 10^-3 Wb, where t is in second. The emf induced in the coil at t = 3s is

• 0.7 V

• 1.2 V

• 0.8 V

• 0.9 V

A beam of light travelling along X-axis is described by the electric field E_v = 600 $\frac{\mathrm{V}}{\mathrm{m}}$. sin$\mathrm{\omega } \left(\mathrm{t} - \frac{\mathrm{x}}{\mathrm{c}}\right)$, the maximum magnetic force on a charge q = 2e, moving along Y-axis with the speed of 3 × 10⁸ m/s is 

• 19.2 × 10^-17 N

• 1.92 × 10^-17

• 0.192

• None of these

An L-C-R series circuit with a resistance of 100 Ω is connected to 200 V (AC source) and angular frequency 300 rad/s. When only the capacitor is removed, then the current lags behind the voltage by 60°. When only the inductor is removed the current leads the voltage by 60°. The average power dissipated in original L-C-R circuit is

• 50 W

• 100 W

• 200 W

• 400 W

In an LCR circuit as shown in figure, both switches are open initially. Now switch S₁ is closed, S₂ kept open. (q is charge on the capacitor and τ = RC is capacitive time constant). Which of the following statement is correct?       

• At t = $\frac{\mathrm{\tau }}{2}$, q = CV ( 1 $-$ e^-1 )

• Work done by the battery is half of the energy dissipated in the resistor

• At t = τ, q = CV/2

• At t = τ, q = CV ( 1 $-$ e^-2 )

A circular coil of radius 10 cm, 500 turns and resistance 2 Ω is placed with its plane perpendicular to the horizontal component of the earth's magnetic field. It is rotated about its vertical diameter through 180° in 0.25 s. The
current induced in the coil is

(Horizontal component of the earth's magnetic field at that place is 3.0 x 10^-5 T)

• 1.9 × 10^-3 A

• 2.9 × 10^-3 A

• 3.9 × 10^-3 A

• 4.9 × 10^-3 A

A series resonant LCR circuit has a quality factor ( Q-factor) 0.4. If  R = 2 kΩ,  C = 0.1 μF, then the value of inductance is

• 0.1 H

• 0.064 H

• 2 H

• 5 H

Assertion:  At resonance, LCR series circuit have a minimum current. 

Reason:  At resonance, in LCR series circuit, the current  and  e.m.f are not in phase with each other.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.