he figure below shows an ac generator connected to a \"black box\" through a pai

Question

he figure below shows an ac generator connected to a "black box" through a pair of terminals. The box contains an RLC circuit, possibly even a multiloop circuit, whose elements and connections we do not know. Measurements outside the box reveal the following relationships.

(a) What is the power factor?
______________

(b) Select all that apply.

The current leads the emf.

The current lags the emf.The circuit in the box is largely inductive.

The circuit in the box is largely capacitive.The circuit in the box is in resonance.

The circuit in the box is not in resonance.

There must be a capacitor in the box.

There need not be a capacitor in the box.

There must be an inductor in the box.

There need not be an inductor in the box.

There must be a resistor in the box.

There need not be a resistor in the box.

(c) At what average rate is energy delivered to the box by the generator?
______________ W

Explanation / Answer

Here ,

part A)

angle between voltage and current

theta = 41 degree

Power factor = cos(theta)

Power factor = cos(41)

Power factor = 0.755

the Power factor is 0.755

b)

as the currrent has more phase constant angle than the voltage applied

the correct options are :

The current leads the emf.

The circuit in the box is not in resonance.

There must be a capacitor in the box.

There must be a resistor in the box.

c)

average rate of power dissipated = Vrms * Irms * power factor

average rate of power dissipated = 77/sqrt(2) * 1.1/sqrt(2) * 0.755

average rate of power dissipated = 32 W

the average rate of power dissipated is 32 W

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