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Chapter 3: Q 3.5-4E (page 121)

If the resistance in the RLcircuit of Figure 3.13(a) is zero, show that the current I (t) is directly proportional to the integral of the applied voltage E(t). Similarly, show that if the resistance in the RCcircuit of Figure 3.13(b) is zero, the current is directly proportional to the derivative of the applied voltage.

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Step by step solution

01

Show that I is directly proportional to the integral of the applied voltage

Apply Kirchhoff’s voltage law for RL circuit is dIdt+RIL=E(t)L.

When R = 0 then equation becomes.

dIdt=E(t)L∫dI=∫1LE(t)dtI=∫1LE(t)dt

Hence it is proved that the current I (t) is directly proportional to the integral of the applied voltage E(t).

02

Evaluate current is directly proportion to the derivative of the applied voltage.

Apply Kirchhoff’s voltage law for RL circuit isRI+qC=E(t)

When R = 0 then equation is

qC=E(t)q=CE(t)I=dqdtI=d(CE(t)dtI=Cd(E(t)dt

Hence it is proved that the current is directly proportional to the derivative of the applied voltage.

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