Ask & Answer Question

Alternating Current Physics Ncert Solutions Class 12th Physics Class 12th Alternating Current Overview

7.13 A coil of inductance 0.50 H and resistance 100 Ω is connected to a 240 V, 50 Hz ac supply.

(a) What is the maximum current in the coil?

(b) What is the time lag between the voltage maximum and the current maximum?

2 Views | Posted 5 months ago

Asked by Shiksha User

1 Answer

Answered by

Payal Gupta | Contributor-Level 10

5 months ago

7.13 Inductance of the Inductor, L = 0.50 H

Resistance of the resistor, R = 100 Ω

Potential of supply voltage, V = 240 V

Frequency of the supply, $ν$ = 50 Hz

Peak voltage is given as $V_{0}$ = $\sqrt[]{2 V} = \sqrt[]{2} \times 240$ = 339.41 V

Angular frequency of the supply, $ω = 2 π ν$ = 2 $π \times 50 = 314.16 r a d / s$

Maximum current in the supply is given as

$I_{0}$ = $\frac{V_{0}}{\sqrt[]{R^{2} + {(ω L)}^{2}}}$ = $\frac{339.41}{\sqrt[]{100^{2} + {(314.16 \times 0.50)}^{2}}}$ = 1.82 A

Equation for voltage is given as V = $V_{0}$ $\cos ? ω t$ and equation for current is given as

I = $I_{0} \cos ? (ω t - \emptyset)$ , where $\emptyset =$ phase difference between voltage and current.

At time t = 0, V = $V_{0}$ [Maximum voltage condition]

For $ω t - \emptyset$ = 0, I = $I_{0}$ [ Maximum current cond

...more

7.13 Inductance of the Inductor, L = 0.50 H

Resistance of the resistor, R = 100 Ω

Potential of supply voltage, V = 240 V

Frequency of the supply, $ν$ = 50 Hz

Peak voltage is given as $V_{0}$ = $\sqrt[]{2 V} = \sqrt[]{2} \times 240$ = 339.41 V

Angular frequency of the supply, $ω = 2 π ν$ = 2 $π \times 50 = 314.16 r a d / s$

Maximum current in the supply is given as

$I_{0}$ = $\frac{V_{0}}{\sqrt[]{R^{2} + {(ω L)}^{2}}}$ = $\frac{339.41}{\sqrt[]{100^{2} + {(314.16 \times 0.50)}^{2}}}$ = 1.82 A

Equation for voltage is given as V = $V_{0}$ $\cos ? ω t$ and equation for current is given as

I = $I_{0} \cos ? (ω t - \emptyset)$ , where $\emptyset =$ phase difference between voltage and current.

At time t = 0, V = $V_{0}$ [Maximum voltage condition]

For $ω t - \emptyset$ = 0, I = $I_{0}$ [ Maximum current condition], for that t = $\frac{\emptyset}{ω}$

Hence the time lag between maximum voltage and maximum current is $\frac{\emptyset}{ω}$

Phase angle is also given by the relation,

$\tan ? \emptyset$ = $\frac{ω L}{R}$ = $\frac{314.16 \times 0.5}{100}$ = 1.5708

$\emptyset = 57.52 °$

= $\frac{57.52 \times π}{180}$ rad = 1.003 rad

$ω t = 1.003$

t = $\frac{1.003}{ω}$ = $\frac{1.003}{314.16}$ = 3.20 $\times 10^{- 3}$ s = 3.2 ms

Hence the time lag between maximum voltage and maximum current is 3.2 ms.

less

0 Upvotes 0 Downvotes

7.13 A coil of inductance 0.50 H and resistance 100 Ω is connected to a 240 V, 50 Hz ac supply.

(a) What is the maximum current in the coil?

(b) What is the time lag between the voltage maximum and the current maximum?

1 Answer

Similar Questions for you

Learn more about...

Most viewed information

Share Your College Life Experience

Didn't find the answer you were looking for?

Need guidance on career and education? Ask our experts

Your Question

7.13 A coil of inductance 0.50 H and resistance 100 Ω is connected to a 240 V, 50 Hz ac supply. (a) What is the maximum current in the coil? (b) What is the time lag between the voltage maximum and the current maximum?

1 Answer

Similar Questions for you

Learn more about...

Most viewed information

Share Your College Life Experience

Didn't find the answer you were looking for?

Need guidance on career and education? Ask our experts

Your Question

7.13 A coil of inductance 0.50 H and resistance 100 Ω is connected to a 240 V, 50 Hz ac supply.

(a) What is the maximum current in the coil?

(b) What is the time lag between the voltage maximum and the current maximum?