# Alternating Currents Nootan Solutions ISC Class-12 Physics Nageen Prakashan

Alternating Currents Nootan Solutions ISC Class-12 Physics Nageen Prakashan Chapter-12 Solved Numericals. Step by step Solutions of Kumar and Mittal ISC Physics Class-12 Nageen Prakashan Numericals Questions. Visit official Website CISCE for detail information about ISC Board Class-12 Physics.

## Alternating Currents Nootan Solutions ISC Class-12 Physics Nageen Prakashan Chapter-12 Solved Numericals

Class: | 12 |

Subject: | Physics |

Chapter 12: | Alternating Current |

Board | ISC |

Writer /Publications | Nootan / Nageen Prakashan/Kumar and Mittal |

Topics | Solved Numericals of page – 575, 576, 577, 578, 579 |

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Alternating Currents Nootan Solutions ISC Class-12 Physics Nageen Prakashan Chapter-12 Solved Numericals

**Transient Current**

An electric current which vary for a small finite time, while growing from zero to maximum or decaying from maximum to zero, is called a transient current.

**Growth of Current in an Inductor**

Growth of current in an inductor at any instant of time t is given by

I = I_{o}(1 – e ^{-Rt / L})

where, I_{o} = maximum current, L = self inductance of the inductor and R = resistance of the circuit.

Here R / L = τ, is called time constant of a L – R circuit.

Time constant of a L – R circuit is the time in which current in the circuit grows to 63.2% of the maximum value of current.

Decay of current in an inductor at any time t is given by

I = I_{o}e ^{-Rt / L}

Time constant of a L – R circuit is the time in which current decays to 36.8% of the maximum value of current.

**Charging and Discharging of a Capacitor**

The instantaneous charge on a capacitor on charging at any instant of time t is given by

q = q_{o}(1 – e ^{– t / RC})

where RC = τ, is called time constant of a R – C circuit.

The instantaneous charge on a capacitor in discharging at any instant of time t is given by q = q_{o}e ^{– t / RC}

Time constant of a R – C circuit is the time in which charge in the capacitor grows to 63.8% or decay to 36.8% of the maximum charge on capacitor.

**Alternating Current**

An electric current whose magnitude changes continuously with time and changes its direction periodically, is called an alternating current.

The instantaneous value of alternating current at any instant of time t is given by

I = I_{o} sin ωt

**Impedance**

The opposition offered by an AC circuit containing more than one out of three components L, C and R, is called impedance (Z) of the circuit.

Impedance of an AC circuit, Z = √R^{2} + (X_{L} – X_{C})^{2}

Its SI unit is ohm.

**Power in an AC Circuit**

The power is defined as the rate at which work is being in the circuit.

The average power in an AC circuit,

P_{av} = V_{rms} i_{rms} cos θ

= V / √2 i / √2 cos θ = Vi / √2 cos θ

where, cos θ = Resistance(R) / Impedance (Z) is called the power factor 0f AC circuit.

### Alternating Currents Nootan Solutions ISC Class-12 Physics Nageen Prakashan Chapter-12 Solved Numericals

Page – 575, 576, 577, 578, 579

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