Question

An RL circuit consists of a 44.0 Ω resistor and a 2.20 mH inductor. Find its impedance Z at 60.0 Hz and 10.0 kHz. (Enter your answers in ohms to at least four significant figures.)

Answer 1

Answer:

44 ohm, 145 ohm

Explanation:

R = 44 ohm, L = 2.2 mH = 2.2 x 10^-3 H

At f = 60 Hz

XL = 2 π f L = 2 x 3.14 x 60 x 2.2 x 10^-3 = 0.82896 ohm

Impedance,  $Z=\sqrt{R^{2}+X_{L}^{2}}$

$Z=\sqrt{44^{2}+0.82896^{2}}$

Z = 44 ohm

At f = 10 kHz = 10000 Hz

XL = 2 π f L = 2 x 3.14 x 10000 x 2.2 x 10^-3 = 138.16 ohm

Impedance,  $Z=\sqrt{R^{2}+X_{L}^{2}}$

$Z=\sqrt{44^{2}+138.16^{2}}$

Z =1 45 ohm

Answer 2

The impedance of the RL circuit at 60 Hz is 44.01 ohms.

The impedance of the RL circuit at 10 kHz is 145.06 ohms.

Impedance of the circuit

The impedance of the RL circuit is the overall opposition to the flow of current.

$Z = \sqrt{R^2 + X_L^2}$

where;

• Xl is the inductive reactance

Xl = ωL

Xl = 2πfL

when, the frequency = 60 Hz

Xl = 2π x 60 x 2.2 x 10⁻³ = 0.829 ohm

when, the frequency = 10 kHz

Xl =  2π x 10,000 x 2.2 x 10⁻³ = 138.23 ohms

Impedance of circuit at 60 Hz

$Z = \sqrt{44^2 + 0.829^2} \\\\Z = 44.01 \ ohms$

Impedance of circuit at 10 kHz

$Z = \sqrt{44^2 + 138.23^2} \\\\Z = 145.06 \ ohms$

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