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

Part(a)Step 1: Given information

We have been given that,

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

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

Part (a) Step 2: Simplify

Let inductive reactance is, $X_{L}$

We know that in inductive circuit reactance is given as,

localid="1649932325839" $X_{L} = 2 π \times f_{1} \times L X_{L} = 2 \times 3 \cdot 14 \times 100 \times 20 \times 10^{- 3} X_{L} = 12 \cdot 57 Ω$

By ohm's law, we know that,

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

Hence, Current is $0.79 A$

Part (b) Step 1: Given information

We have been given that,

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

Part (b) Step 2: Simplify

Let inductive reactance is, $X_{L}$

We know that in inductive circuit reactance is given as,

localid="1649932419844" $X_{L} = 2 π \times f_{1} \times L X_{L} = 2 \times 3 \cdot 14 \times 100 \times 10^{3} \times 20 \times 10^{- 3} X_{L} = 12566 Ω$

By ohm's law, we know that,

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

Hence, Current is $0.00079 A$ $0 \cdot 00079 A$

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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

Step by step solution

Part(a)Step 1: Given information

Part (a) Step 2: Simplify

Part (b) Step 1: Given information

Part (b) Step 2: Simplify

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A 20mHinductor is connected across an AC generator that produces a peak voltage of 10V. What is the peak current through the inductor if the emf frequency is (a) 100Hz? (b) 100kHz?

Short Answer

Step by step solution

Part(a)Step 1: Given information

Part (a) Step 2: Simplify

Part (b) Step 1: Given information

Part (b) Step 2: Simplify

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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) $100 k H z$ ?