Question

The current in a device varies with time t as I = 6 t, where I is in mA and t is in s. The amount of charge that passes through the device from t = 0s to t = 3s is ______.

पर्याय

• 10 mC

• 18 mC

• 27 mC

• 54 mC

Answer 1

The current in a device varies with time t as I = 6 t, where I is in mA and t is in s. The amount of charge that passes through the device from t = 0s to t = 3s is 27 mC.

Explanation:

Given: I = 6t

where I is the current and t is the time.

The time range is 0 < t < 3 sec.

We know that `I = q/t` so we need to find q.

Differentiating both sides,

`I = (dq)/(dt)`

⇒ `6t = (dq)/(dt)`

`dq = 6t xx dt`

⇒ `q = int_0^3 6t  dt`

⇒ `q = 6 int_0^3t dt`

⇒ `q = 6 xx [t^2/2]_0^3`

⇒ `q = 6 xx 3^2/2`

⇒ q = 27 μC