Question

the charge = 3-4t^2 across a resistor in time 2sec what is the heat produced

Answer 1

Explanation:

Correct option is

A

22C

Step 1: Current through the wire

We know that,

I=

dt

dq

⇒dq=I dt ....(1)

Step 2: Integrating the equation (1) with proper limits

Time interval: t=0s to t=2s

∫dq=∫

0

2

Idt

I=3t

2

+2t+5

⇒q=∫

0

2

(3t

2

+2t+5)dt=[t

3

+t

2

+5t]

0

2

=(8+4+10)=22C

Hence Option (A) is correct.

Answer 2

Explanation:

the amount of heat produced for 2s of time is 341.3J.

Explanation:

Given the resistance of the resistor,

The charge is given by,

Electric current is defined as the rate of flow of charge.

This can be written as,

Substituting the charge and differentiating with respect to time,

According Joule's law of heating, the amount of heat produced in a current carrying conductor in a time t is given by

Integrating on both sides and substituting the respective values