An electrical device draws 2 kW, 50 kV power from AC mains voltage 223 V ( r m s ) . The current differs (lags) in phase by ϕ tan ϕ = - 3 4 as compared to voltage. Find (i) R , (ii) X C - X L , and (iii) I M . Another device has twice the values for R , X C and X L . How are the answers affected?

P o w e r P = V 2 Z ⇒ 50 , 000 2000 = 25 = Z Z 2 = R 2 + X C - X L 2 = 625 tan ϕ = X C - X L R = - 3 4 625 = R 2 + - 3 4 R 2 = 25 16 R 2 = 400 ⇒ R = 20 Ω X C - X L = - 15 Ω I = V Z = 223 25 ≃ 9 A . I M = 2 × 9 = 12 . 6 A . If R , X C , X L are all doubled, tan ϕ does not change. Z is doubled, current is halved. Power drawn is halved.

For an L C R circuit driven at frequency ω, the equation reads L d i d t + R i + q C = v t = v m sin ω t Multiply the equation by i and simplify where possible.

L t d t d t + R t 2 + q t c = v t ; L t d t d t = d d t 1 2 L t 2 = rate of change of energy stored in an inductor. R i 2 = joule heating loss q C t = d d t q 2 2 C = rate of change of energy stored in the capacitor. v t = rate at which driving force pours in energy. It goes into (i) ohmic loss and (ii) increase of stored energy. ∫ 0 T d t d d t 1 2 t 2 + q 2 C + ∫ 0 T R t 2 d t = ∫ 0 T v t d t 0 + + v e = ∫ 0 T v t d t ∫ 0 T v t d t > 0 if phase difference, a constant is acute.

EASY

12th CBSE

IMPORTANT

Earn 100

A coil of $0.01$ henry inductance and $1$ ohm resistance is connected to $200$ volt, $50 H z$ ac supply. Find the impedance of the circuit and time lag between max. alternating voltage and current.

Important Questions on Alternating Current

MEDIUM

12th CBSE

IMPORTANT

NCERT Exemplar Physics - Class 12>Chapter 7 - Alternating Current>SA>Q 7.24

60 W

load is connected to the secondary of a transformer whose primary draws line voltage. If a current of

0.54 A

flows in the load, what is the current in the primary coil? Comment on the type of transformer being used.

MEDIUM

12th CBSE

IMPORTANT

NCERT Exemplar Physics - Class 12>Chapter 7 - Alternating Current>SA>Q 7.25

Explain why the reactance provided by a capacitor to an alternating current decreases with increasing frequency.

MEDIUM

12th CBSE

IMPORTANT

NCERT Exemplar Physics - Class 12>Chapter 7 - Alternating Current>SA>Q 7.26

Explain why the reactance offered by an inductor increases with the increasing frequency of an alternating voltage.

HARD

12th CBSE

IMPORTANT

NCERT Exemplar Physics - Class 12>Chapter 7 - Alternating Current>LA>Q 7.27

An electrical device draws

2 kW, 50 kV

power from AC mains voltage

223 V (r m s)

. The current differs (lags) in phase by

ϕ (\tan ϕ = \frac{- 3}{4})

as compared to voltage. Find (i)

R

, (ii)

X_{C} - X_{L}

, and (iii)

I_{M}

. Another device has twice the values for

R, X_{C}

and

X_{L}

. How are the answers affected?

MEDIUM

12th CBSE

IMPORTANT

NCERT Exemplar Physics - Class 12>Chapter 7 - Alternating Current>LA>Q 7.28

1 MW

power is to be delivered from a power station to a town

10 km

away. One uses a pair of

Cu

wires of radius

0.5 c m

for this purpose. Calculate the fraction of ohmic losses to the power transmitted if
(i) power is transmitted at

220 V

. Comment on the feasibility of doing this.

MEDIUM

12th CBSE

IMPORTANT

NCERT Exemplar Physics - Class 12>Chapter 7 - Alternating Current>LA>Q 7.28

$1 MW$ power is to be delivered from a power station to a town $10 km$ away. One uses a pair of $Cu$ wires of radius $0.5 c m$ for this purpose. Calculate the fraction of ohmic losses to the power transmitted if
(ii) a step-up transformer is used to boost the voltage to $11000 V$ , power transmitted, then a step-down transformer is used to bring the voltage to $220 V$ .

MEDIUM

12th CBSE

IMPORTANT

NCERT Exemplar Physics - Class 12>Chapter 7 - Alternating Current>LA>Q 7.29

Consider the $L C R$ circuit shown in Fig 7.6. Find the net current $i$ and the phase of $i$ . Show that $i = \frac{v}{Z}$ .
Find the impedence $Z$ for this circuit.

Question Image

HARD

12th CBSE

IMPORTANT

NCERT Exemplar Physics - Class 12>Chapter 7 - Alternating Current>LA>Q 7.3

For an $L C R$ circuit driven at frequency ω, the equation reads

$L \frac{d i}{d t} + R i + \frac{q}{C} = v_{t} = v_{m} \sin ω t$

Multiply the equation by i and simplify where possible.

A coil of 0.01 henry inductance and 1 ohm resistance is connected to 200 volt, 50 Hz ac supply. Find the impedance of the circuit and time lag between max. alternating voltage and current.

Important Questions on Alternating Current

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A coil of $0.01$ henry inductance and $1$ ohm resistance is connected to $200$ volt, $50 H z$ ac supply. Find the impedance of the circuit and time lag between max. alternating voltage and current.