THANK YOU in advance! Parts a through f are all part of the same problem. 2. At

Question

THANK YOU in advance! Parts a through f are all part of the same problem.

2. At the right is a schematic circuit diagram showing a resistor, capacitor, inductor and alternating voltage source is (t) (a) Label these with R, C, L and a.c. It is important to know that (i) The same current flows at each instant through each circuit element. This means the current through the capacitor i (t) is the same at each instant as the current i,(0) through the resistor C000 (ii) the sum at each instant of the voltage drops around the circuit is zero. Thus if ,(c) is the voltage drop across the capactor, (1) is the voltage drop across the resistor and is the EMF Av,1) provided at the same instant by the signal generator, then at each instant in time

Explanation / Answer

part a:

in the clockwise direction, the elements are AC source, Resistor R,capacitor C and inductor L.

part b:

capacitor top plate:

will have positive charge when current is flowing in the shown direction in the figure.

capacitor bottom plate:

will have negative charge when current is flowing in the shown direction in the figure.

part c:

voltage drop across the inductor =L*(di/dt)

part d:

capacitor voltage is given by

q=c*(dV/dt)

==>V=(1/c)*integration of (q*dt)

part e:

voltage drop across the resistor=i*R

part f:

using KVL , voltgae drop across the loop is zero.

Vs(t)-L*(di/dt)-((1/c)*integration of q*dt)-i*R=0

=> Vs(t)=L*(di/dt)+(1/c)*integration of q*dt + i*R

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