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_oe ^{-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_oe ^{– 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 = √R² + (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.