Question

An ac series circuit has an impedance of 192 Ω, and the phase angle between the current and the voltage of the generator is ϕ = −75°. The circuit contains a resistor and either a capacitor or an inductor. Find the resistance R and the capacitive reactance XC or the inductive reactance XL, whichever is appropriate.

Answer 1

Answer:

Resistance = 49.69 ohm

Capacitive reactance / inductive reactance = 185.45 ohm

Explanation:

We have given impedance of the circuit = 192 ohm

Angle between voltage and current $\Phi =-75^{\circ}$

Power factor $=cos(-75^{\circ})=0.2588$

We know that power factor is given by $cos\Phi =\frac{R}{Z}$

$0.2588=\frac{R}{192}$

$R=49.693ohm$

Impedance is given by $Z=\sqrt{R^2+(X_L/X_C)^2}$

$192=\sqrt{49.693^2+(X_L/X_C)^2}$

Squaring both side $36864=2469.419+(X_L/X_C)^2$

$X_L/X_C=185.457ohm$

Answer 2

The resistance R and the capacitive reactance XC or the inductive reactance XL is mathematically given as

• R=49.7
• X_L/X_C=185.457ohm

Question Parameters:

An ac series circuit has an impedance of 192 Ω,

the current and the voltage of the generator is ϕ = −75°.

given power factor to be 0.2588

and

$cos\phi =\frac{R}{Z}\\\\0.2588=\frac{R}{192}$

R=49.7

Generally the equation for the Impedance   is mathematically given as

$Z=\sqrt{R^2+(X_L/X_C)^2}$

Therefore

$192=\sqrt{49.693^2+(X_L/X_C)^2}$

X_L/X_C=185.457ohm

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