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Chapter 32: Q. 22 (page 924)

A $20 m H$ inductor is connected across an AC generator that produces a peak voltage of $10 V$ . What is the peak current through the inductor if the emf frequency is (a) $100 H z$ ? (b) $100 k H z$ ?

Short Answer

Expert verified

(a) Peak current is $0.79 A$

(b) Peak current is $0.00079 A$

Step by step solution

01

Part(a)Step 1: Given information

We have been given that,

Inductance of inductor is, $L = 20 m H = 20 脳 10^{- 3} H$

Peak Voltage is, $V_{0} = 10 V$ and frequency $f_{1} = 100 H z$

02

Part (a) Step 2: Simplify

Let inductive reactance is, $X_{L}$

We know that in inductive circuit reactance is given as,

localid="1649932325839" $X_{L} = 2 蟺脳 f_{1} 脳 L X_{L} = 2 脳 3 路 14 脳 100 脳 20 脳 10^{- 3} X_{L} = 12 路 57 惟$

By ohm's law, we know that,

$C u r r e n t, I = \frac{V_{o}}{X_{L}} I = \frac{10}{12 路 57} I = 0 路 79 A$

Hence, Current is $0.79 A$

03

Part (b) Step 1: Given information

We have been given that,

Frequency is, $f_{1} = 100 k H z = 100 脳 10^{3} H z$

04

Part (b) Step 2: Simplify

Let inductive reactance is, $X_{L}$

We know that in inductive circuit reactance is given as,

localid="1649932419844" $X_{L} = 2 蟺脳 f_{1} 脳 L X_{L} = 2 脳 3 路 14 脳 100 脳 10^{3} 脳 20 脳 10^{- 3} X_{L} = 12566 惟$

By ohm's law, we know that,

$C u r r e n t, I = \frac{V_{o}}{X_{L}} I = \frac{10}{12566} I = 0 路 00079 A$

Hence, Current is $0.00079 A$ $0 路 00079 A$

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Most popular questions from this chapter

a. Evaluate $V_{R}$ in figure at emf frequencies $100, 300, 1000, 3000, 10000 H z$

b. Graph $V_{R}$ versus frequency. Draw a smooth curve through your five points.

a. Show that the average power loss in a series RLC circuit is

$P_{a v g} = \frac{蝇^{2} {(蔚_{r m s})}^{2} R}{蝇^{2} R^{2} + L^{2} {(蝇^{2} - 蝇_{o}^{2})}^{2}}$

b. Prove that the energy dissipation is a maximum at $蝇 = 蝇_{o}$ .

$F I G U R E E X 32.9$ shows voltage and current graphs for a capacitor.

a. What is the emf frequency $f$ ?

b. What is the value of the capacitance $C$ ?

The emf phasor in FIGURE EX32.2 is shown at $t = 15 m s$ .

a. What is the angular frequency $蝇$ ? Assume this is the first rotation.

b. What is the instantaneous value of the emf?

A series $R L$ circuit is built with a role="math" localid="1650111235060" $110 鈩�$ resistor and a $5.0 - c m -$ long, $1.0 - c m -$ diameter solenoid with $800$ turns of wire. What is the peak magnetic flux through the solenoid if the circuit is driven by a $12 V, 5.0 k H z$ source?

See all solutions

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