An alternating voltage and the corresponding current in a circuit are given by ε = 110 sin ⁡ ω t + π 6 and I = 5 sin ⁡ ω t - π 6 respectively. Find the impedance and the average power dissipation in it.

Given, Voltage in the circuit ε = 110 sin ⁡ ω t + π 6 Comparing with ε = ε 0 sin ⁡ ω t + δ 1 ε 0 = 110 V , δ 1 = π 6 Current in the circuit I = 5 sin ⁡ ω t - π 6 Comparing with I = I 0 sin ⁡ ω t + δ 2 I 0 = 5 A , δ 2 = - π 6 Phase difference between voltage and current ϕ = δ 1 - δ 2 = π 3 Impedance of the circuit Z = ε 0 I 0 = 110 5 = 22 Ω Average power dissipated P a v g = ε 0 I 0 2 cos ϕ P a v g = 110 × 5 2 × cos π 3 = 137.5 W

(i) Find the value of the phase difference between the current and the voltage in the series LCR circuit shown below. Which one leads in phase: current or voltage? (ii) Without making any other change, find the value of the additional capacitor C 1 , to be connected in parallel with the capacitor C, in order to make the power factor of the circuit unity.

Given, Inductance of the circuit L = 100 m H Capacitance of the circuit C = 2 μ F Resistance of the circuit R = 400 Ω Voltage of the source V = V 0 sin 1000 t + ϕ So, angular frequency, ω = 1000 r a d s - 1 . Inductive reactance X L = ω L = 1000 × 100 × 10 - 3 Ω = 100 Ω . Capacitive reactance X C = 1 ω C = 1 1000 × 2 × 10 - 6 Ω = 500 Ω . (i) Phase value ϕ between current and voltage is given by, tan ⁡ ϕ = X L - X C R = 100 - 500 400 = - 1 ⇒ ϕ = - π 4 ϕ is negative, implies X L > X C or the current leads the voltage by π / 4 rad. (ii) Power factor is unity when X C = X L or 1 ω C ' = 100 Ω ⇒ C ' = 1 100 ω = 1 100 × 1000 F = 10 μ F ⇒ C ' = C + C 1 or 10 = 2 + C 1 ∴ Required capacitance need to be added C 1 = 8 μ F .

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12th CBSE

IMPORTANT

Earn 100

An a.c. circuit has a resistance and an inductance connected in series as shown in figure. Calculate the current and the power factor in the circuit.

Important Questions on Alternating Current and Electrical Machines

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12th CBSE

IMPORTANT

PHYSICS A Reference Book for Class 12 Volume 2>Chapter 1 - Alternating Current and Electrical Machines>Problems For Practice>Q 4

Calculate the current and power factor of the circuit shown in figure.

Question Image

MEDIUM

12th CBSE

IMPORTANT

PHYSICS A Reference Book for Class 12 Volume 2>Chapter 1 - Alternating Current and Electrical Machines>Problems For Practice>Q 5

In the circuit shown in figure, the potential differences across resistance, capacitance and inductance are given. Find the emf of the source of alternating current and power factor of the circuit.

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12th CBSE

IMPORTANT

PHYSICS A Reference Book for Class 12 Volume 2>Chapter 1 - Alternating Current and Electrical Machines>Problems For Practice>Q 6

A group of electric bulbs has a power rating of

300 W

. An a.c. voltage,

V = 141.4 s i n (314 t + π / 3)

is applied to the group. Calculate the effective current.

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12th CBSE

IMPORTANT

PHYSICS A Reference Book for Class 12 Volume 2>Chapter 1 - Alternating Current and Electrical Machines>Problems For Practice>Q 7

An alternating voltage and the corresponding current in a circuit are given by

ε = 110 \sin (ω t + \frac{π}{6})

and

I = 5 \sin (ω t - \frac{π}{6})

respectively. Find the impedance and the average power dissipation in it.

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12th CBSE

IMPORTANT

PHYSICS A Reference Book for Class 12 Volume 2>Chapter 1 - Alternating Current and Electrical Machines>Problems For Practice>Q 8

An inductor

200 m H

, capacitor

500 μ F

, resistor

10 Ω

are connected in series with a

100 V

, variable frequency a.c. source. Calculate the (i) frequency at which the power factor of the circuit is unity, (ii) current amplitude at this frequency, (iii) Q-factor.

MEDIUM

12th CBSE

IMPORTANT

PHYSICS A Reference Book for Class 12 Volume 2>Chapter 1 - Alternating Current and Electrical Machines>Problems For Practice>Q 9

An inductor of unknown value, a capacitor of

100 μ F

and a resistor of

10 Ω

are connected in series to a

200 V

50 H z

a.c. source. It is found that the power factor of the circuit is unity. Calculate the inductance of the inductor and the current amplitude.

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12th CBSE

IMPORTANT

PHYSICS A Reference Book for Class 12 Volume 2>Chapter 1 - Alternating Current and Electrical Machines>Problems For Practice>Q 10

(i) Find the value of the phase difference between the current and the voltage in the series LCR circuit shown below. Which one leads in phase: current or voltage?

Question Image

(ii) Without making any other change, find the value of the additional capacitor $C_{1}$ , to be connected in parallel with the capacitor C, in order to make the power factor of the circuit unity.

HARD

12th CBSE

IMPORTANT

PHYSICS A Reference Book for Class 12 Volume 2>Chapter 1 - Alternating Current and Electrical Machines>Problems For Practice>Q 11

A circuit containing a

80 m H

inductor and a

60 μ F

capacitor in series is connected to a

230 V

50 H z

supply. If the circuit has a resistance of

15 Ω

, obtain the average power transferred to each element of the circuit and the total power absorbed.

An a.c. circuit has a resistance and an inductance connected in series as shown in figure. Calculate the current and the power factor in the circuit.

Important Questions on Alternating Current and Electrical Machines

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