Question

The total charge entering a terminal is given by q=5t sin4pie t.calculate the current at t=0.5sec

Answer 1

i= dq/dt =d/dt (5t sin 4π t) mC/s =(5t sin 4π t +20πt cos 4π t)mA

At=0.5

i=5 sin 2 π +10π cas 2π=31.42mA

Answer 2

Concept introduction:

This question is based on the identification of the current flowing across a terminal with total charge 5t sin4pie t. Charge is calculated by q = W/V.

Given:

We have been given the total charge entering the terminal along with the time.

To find:

We have to calculate the current flowing in the terminal.

Solution:

As per the question,

i=dtdq=dtd(5tsin4πt)mC/s

=(5sin4πt+20πtcos4πt) mA

At t = 0.5,

i= 5 \sin {2 \pi} + 10 \pi \cos {2 \pi}

= 0 + 10 \pi

= 31.42i

Therefore, 5sin2π+10πcos2π=0+10π=31.42 mA

Final answer:

Current flowing in the terminal is 31.42mA

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