# AC Circuits

(a)

A particular 240V, 50Hz electrical appliance is rated at 2kW and has a lagging power factor of 0.7.

(i)

Determine the appliance's power factor when it is used on a 60Hz supply.

(ii)

Calculate the supply voltage required to maintain the appliance at its rated power when operated off a 60Hz supply.

(b)

When placed in series a coil and capacitor resonate at a frequency of 2251Hz and when placed in parallel they resonate at a frequency of 2228Hz. At parallel resonance it is also found that a current of 5mA flows from the supply when the supply voltage is 25V r.m.s.

Determine the value of the capacitor and the inductance and the resistance of the coil.

I've also attached this problem as a Word document to allow super/subscripts.

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#### Solution Preview

Hi,

** Please see the attached file for the complete solution response **

(a)

A particular 240V, 50Hz electrical appliance is rated at 2kW and has a lagging power factor of 0.7.

(i)

Determine the appliance's power factor when it is used on a 60Hz supply.

Solution: The phase shift of the apparent power to the real power is:

(please see the attached file)

And the relationship of the real power and the reactive power is:

(please see the attached file)

Substituting the values, we have:

(please see the attached file)

The inductive reactance can be computed by using the formula:

(please see the attached file)

Solving, we have:

(please see the attached file)

From the inductive reactance, we can ...

#### Solution Summary

This solution provides a detailed, step-by-step explanation to the given circuit problems.