- Introduction
- |
- Alternating current and Alternating EMF
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- Average or mean current
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- Root Mean square value of AC
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- Phasor diagram
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- A.C through pure resistor
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- A.C through pure inductor
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- AC through pure capacitor
- |
- Circuit containing inductance and resistance in series
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- Circuit containing capacitance and resistance in series
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- LCR series circuit

- Figure below shows pure inductor of inductance L connected in series with a resistor of resistance R through sinusoidal voltage

V=V_{0}sin(ωt+φ)

- An alternating current I flowing in the circuit gives rise to voltage drop V
_{R}across the resistor and voltage drop V_{L}across the coil

- Voltage drop V
_{R}across R would be in phase with current but voltage drop across the inductor will lead the current by a phase factor π/2

- Now voltage drop across the resistor R is

V_{R}=IR

and across inductor

V_{L}=I(ωL)

where I is the value of current in the circuit at a given instant of time

- So voltage phasors diagram is

In figure (10) we have taken current as a reference quantity because same amount of current flows through both the components. Thus fro phasors diagram

is known as impedance of the circuit

- Current in steady state is

and it lags behind applied voltage by an angle φ such that

tanφ=ωL/R ---(16)

- Figure below shows a circuit containing capacitor and resistor connected in series through a sinusoidal voltage source of voltage

V=V_{0}sin(ωt+φ)

- In this case instantaneous P.D across R is

V_{R}=IR

and across the capacitor C is

V_{C}=I/ωC

- In this case V
_{R}is in phase with current i and V_{C}lags behind i by a phase angle 90_{0}

- Figure 11(b) shows the phasors diagram where vector OA represent the resultant of V
_{R}and V_{C}which is the applied Voltage thus

is called the impedance of the circuit

- Again from the phasors diagram applied voltage lags behind the current by a phase angle φ given by

tanφ= V_{C}/ V_{R}=1/ωCR ---(18)

Class 12 Maths Class 12 Physics

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