CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Switch S is closed in the circuit at time t=0. Find the current through the capacitor and the inductor at any time t.
1748675_f48e9d5427df4e17b57ade6489c1c9ae.png

Open in App
Solution

Circuit can be analyzed separately
(i) Inductor
ε=ILR3+LdILdt
on ontegrating , we get
IL=ER3(1eR2tL)
(ii) In loop ABCDEFA , εIR1+(II1)R2,
ε+I1R2R1+R2=I
In loop ABGEFA , ε=IR1+qC
ε=((ε+I2R2)R1+R2)R1+qc
Differentiating w.r.t time , we get
0=0+dI1dt×(R1R2R1+R2)+dqdt×1C
dI1dt=(R1+R2R1R2)×1C×I1
dI1I1=(R1+R2R1R2)×1C×dt
[lnI1]I1ε/R1=(R1+R2R1R2)×[t]t0C

( t=0,C acts as a conducting wire)
ln(I1ε/R1)=(R1+R2R1R2)×tC
Ithroughcapacitor=εR1e(R1+R2R1R2)tC

1623131_1748675_ans_25483dc96afd4dc69503f3d091447f91.png

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Maxwell's Equation
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon