Question

The current in a conductor varies with time t as $I=3t+4t^2$, where I is in amperes and t in seconds. The electric charge that flows through the section of the conductor between t = 1 s and t = 3 s is

• A. $\frac{14}{3}C$
• B. $\frac{3}{14}C$
• C. $\frac{140}{3}C$
• D. $\frac{3}{140}C$

Answer 1

The correct option is (A) $\frac{140}{3}C$

Step 1, Given data

Current is varying with time as $I=3t+4t^2$

Step 2, Finding the charge flow

We know,

$I=\frac{Q}{t}$

$Or,I=\frac{dQ}{dt}$

Now we can write

$(3t+4t^2)dt=dQ$

Integrating both sides

${\int }_0^{Q}dQ={\int }_1^3(3t+4t^2)dt$

Or, $Q=3{\left[\frac{t^2}{2}\right]}_1^3+{\left[\frac{t^3}{3}\right]}_1^3$

After solving

Q = $\frac{140}{3}C$

Hence the charge flowing in the given time interval is $\frac{140}{3}C$ .