A resistor and an unknown device are connected in series with an AC generator as

Question

A resistor and an unknown device are connected in series with an AC generator as shown in the diagram below. The current lags behind the voltage of the generator by 61°.

(a) If the total impedance of the circuit is 148 , what is the value of the resistor in the circuit?

(b) What is the reactance of the device?

A resistor and an unknown device are connected in series with an AC generator as shown in the diagram below. The current lags behind the voltage of the generator by 61Â degree . If the total impedance of the circuit is 148 ©, what is the value of the resistor in the circuit? What is the reactance of the device?

Explanation / Answer

Here

arctan(X/R) = 61

Therefore

X/R = 1.804

X = 1.804R -----(1)

Also

sqrt(R^2 + X^2) = 148 ohm

Therefore

R^2 + X^2 = 21904

(1.804R)^2 + R^2 = 21904

R = 71.753 ohm

X = 1.804*71.753

= 129.44 ohm

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