Question

The charge flowing through a resistor R = 2 Q varies with time as q = 3 - 4t². The heat produced in 2 second is about (where q is in C and t is in s)

A)330.3 J

B)341.3 J

C)345.2 J

D)326.4 J​​

Answer 1

Answer:

We can find the current as the derivative of the charge with respect to time:

I = dq/dt = -8t

The power dissipated by the resistor is:

P = I²R = (-8t)²(2) = 128t²

To find the heat produced in 2 seconds, we integrate the power with respect to time from 0 to 2:

Q = ∫₀² P dt = ∫₀² 128t² dt = 128(1/3)t³ ∣₀² = 341.3 J

Therefore, the answer is B) 341.3 J.