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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?

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Payal Gupta | Contributor-Level 10

4 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

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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.

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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?

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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?

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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?