Electrical Circuits

In a series LCR circuit, the instantaneous voltage and current are given by: where and are the peak voltage and current, is the angular frequency, and is the phase difference between the voltage and current.
The instantaneous power ( ) dissipated in the circuit is the product of instantaneous voltage and current: To find the average power ( ) over one complete cycle ( ), we need to find the average value of this expression.
We know the average values over one cycle are:


Therefore, the average power is: We can express this in terms of the root mean square (RMS) values, where and . This is the expression for the average power dissipated in a series LCR circuit. The term is called the power factor.

For an ideal transformer, the ratio of the secondary voltage ( ) to the primary voltage ( ) is equal to the ratio of the number of turns in the secondary coil ( ) to the number of turns in the primary coil ( ). Given:
Primary voltage, V
Secondary voltage, V
Number of turns in primary coil,
Substituting the values: The number of turns in the secondary coil is 4000.

The phase difference ( ) between the voltage and current in a series LCR circuit is given by the formula: Given:
Resistance,
Inductive reactance,
Capacitive reactance,
Substituting the values: Therefore, the phase difference is: Since , the circuit is inductive, and the voltage leads the current by an angle of , which is approximately .