Question 15: AC fundamentals

Question

In the circuit shown in figure, the AC source has angular frequency $$\omega$$ = 2000 rad s$$-$$1. The amplitude of the current will be nearest to

Accepted Answer

Given, $$\omega$$ = 2000 rad s
$$-$$1
L = 5 mH = 5 $$	imes$$ 10
$$-$$3
H
C = 50 $$\mu$$F = 50 $$	imes$$ 10
$$-$$6
F
V = 30 V
Inductive reactance,
X
L
= $$\omega$$L = 2000 $$	imes$$ 5 $$	imes$$ 10
$$-$$3
= 10 $$\Omega$$
and capacitive reactance,
$${X_C} = {1 \over {\omega C}} = {1 \over {50 	imes {{10}^{ - 6}} 	imes 2000}} = {{100} \over {10}} = 10\Omega $$
$$\Rightarrow$$ X
L
= X
C
The given circuit is resonant circuit.
Hence, impedance of circuit, Z = R = 4 + 6 + 0.5 = 10.5$$\Omega$$
Amplitude of current, $${I_0} = {V \over Z} = {{30} \over {10.5}} = 2.85$$ A

Answer

2.85 A

Answer

3 A

Answer

0.5 A

Answer

3.625 A

AC fundamentals

In the circuit shown in figure, the AC source has angular frequency $\omega = 2000 rad s-$1. The amplitude of the current will be nearest to

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