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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)


    AC through Circuit containing inductance and resistance in series

  • 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


    Voltage current phasor diagram for LR circuit

    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

    Circuit containing inductance and resistance in series|Alternating Current
    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)


    AC through Circuit containing capacitance and resistance in series

  • 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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