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Consider the LCR circuit shown in figure find the net current I and the phase of i. show that i=V/Z. find the impedance Z for this circuit.

0 5 Views | Posted 4 months ago
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  • 1 Answer

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    Answered by

    Payal Gupta | Contributor-Level 10

    4 months ago

    This is a long answer type question as classified in NCERT Exemplar

    Total current i=i1+i2

    Vmsinwt=Ri1

    I1= VmsinwtR

    If q2 is charge on the capacitor at any time t then for series combination of C and L

    Applying KVL in below circuit

    So q2=qmsin(wt q2C+Ldi2dt-Vmsinwt=0 )……….1

    qm[ +∅ sin(wt+ q2C+Ld2q2dt2=Vmsinwt )]= Vmsinwt

    if dq2dt=-qmw2sin?(wt+∅)

    qm= usethisvalueineqn1

    from above equation i2= 1C+L(-w2)

    i2= ∅ when ∅=0

    so total current I = i1+i2

    I= Vm(1c-Lw2)

    I= i1+i2= Ccos dq2dt=wqmcos?wt+∅ +Csin wVmcos?(wt+∅)1c-Lw2

    I= Csin(wt+ ∅=0,i2=Vmcoswt1wC-Lw )

    C= VmsinwtR+Vmcoswt1wC-Lw

    ∅sinwt 1/2

    ∅coswt = tan-1 ∅

    A2+B2 1/2

    This is the expression for impedance.2

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