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how to solve questions based on kirchoffs law with capacitors and inductors where in only the capacitance and inductance and the voltage of the battery is given to us .... please illustrate !!!

how to solve questions based on kirchoffs law with capacitors and inductors where in only the capacitance and inductance and the voltage of the battery is given to us .... please illustrate !!!


 

Grade:12th pass

2 Answers

Saurabh Singh
askIITians Faculty 49 Points
7 years ago

179-2439_kirchoff.jpg
now this is the general case .....we have a voltage source, a resistance , a capacitor and an inductor.
Kirchhoff law says that for a mesh the sum of voltages should be zero ( in a loop)
so we start from left side ,
we have a voltage source so we write V(t) -(assuming it may vary with time , this makes our equation flexible)
then we have a resistor so voltage drop will be iR , since its is a drop so we write -iR
then moving towards right we have a capacitor
voltage across a capacitor is simply q/C, so we write -q/C as it is a drop
and finally at the rightmost we have our inductor so its -Ldi/dt
once we have this equation we can solve it using the fact that current is rate of change of charge with time so i=dq/dt
substituting i in the equation we get a second order differential equation in 'q' which is easy to solve.
dear student, this is the generalized method and can be very easily extended to other cases such as only
capacitor or only inductor by setting the values of L and C zero as required.
now you have mentioned we have been given only C, L and V
that is all we need,
we have an equation that gives us 'q' as function of C,L and V
we can put in the values of C,L and V to get the q
once we get the equation of q we can differentiate it with time to get the current
hence our problem is solved


Thanks & Regards

Saurabh Singh,
askIITians Faculty
B.Tech.
IIT Kanpur

saarah thames
33 Points
7 years ago
thank u soo much saurabh sir.. for this wonderful explanation

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