Class 12 Physics Alternating Current | Resistive AC Circuit |

**Resistive AC Circuit**

- In resistive AC circuit there will be only resistors and no other circuit elements will be present.
- Consider the circuit as shown in the (fig) below .
- Input AC voltage V =
_{m}sinωt (equation(1)) - Where V
_{m}= peak value of voltage. It is also known as__voltage amplitude.__

- Let the EMF of the voltage source = V, then by applying Kirchhoff’s loop law to the circuit, total EMF of the circuit will be V = IR
- Where I = current flowing through the circuit.
- Using equation(1), V
_{m}sinωt = IR - => I = (V
_{m}/R) sinωt equation(2) - This is the amount of current which flows through the circuit. By substituting I
_{m}= (V_{m}/R) in equation(2) - Therefore
**I = I**_{m}sinωt - Where I
_{m}=__current amplitude__or peak value of current.

** Conclusion**:-

If alternating voltage is applied to a circuit which has only a resistor then the current flowing through the circuit will also be alternating current.

This means the current flowing through a circuit is also a sinusoidal function.

__Graphical representation of voltage & current__

- From the graph it is clear that although both voltage and current are sinusoidal function but the peak value of current is less than the peak value of voltage. As I
_{m }= (V_{m}/R) => I_{m }< V_{m}. - Voltage and current are in phase with each other which means both of them reach their maximum value, then 0 and their minimum value at the same time.
- Average current over a complete cycle is zero.
- Average voltage over a complete cycle is zero.
- V = V
_{m}sinωt - Where V =
__instantaneous__value of voltage at time t. - I = I
_{m}sinωt - Where I =
__instantaneous__value of current at any time t.

The given graph is showing that in a pure resistor, the voltage and current are in phase. The minima, zero and maxima occur at the same respective times.

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