# Circuit containing inductance and resistance in series|Alternating Current

## (9) Circuit containing inductance and resistance in series

• Figure below shows pure inductor of inductance L connected in series with a resistor of resistance R through sinusoidal voltage
V=V0sin(ωt+φ)

• An alternating current I flowing in the circuit gives rise to voltage drop VR across the resistor and voltage drop VL across the coil
• Voltage drop VR 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
VR=IR
and across inductor
VL=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)

## (10) Circuit containing capacitance and resistance in series

• Figure below shows a circuit containing capacitor and resistor connected in series through a sinusoidal voltage source of voltage
V=V0sin(ωt+φ)

• In this case instantaneous P.D across R is
VR=IR
and across the capacitor C is
VC=I/ωC
• In this case VR is in phase with current i and VC lags behind i by a phase angle 900
• Figure 11(b) shows the phasors diagram where vector OA represent the resultant of VR and VC 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= VC/ VR=1/ωCR                                       ---(18)

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