Question

The current flowing through a wire depends on
time as I = 3t^2+ 2t + 5. The charge flowing through
the cross-section of the wire in time from t = 0 and
t= 2 sec. is
1) 22 C 2 ) 20 C 3) 18 C 4) 5 C

Answer 1

Answer:

(1) 22 C

Explanation:

22 C is the correct answer

by integrating the given value of current and putting the limits we can get the value of charge i.e., 22 C

Answer 2

answer : option (1) 22C

The current flowing through a wire depends on time as I = 3t² + 2t + 5

we know,

current is the rate of change of charge with respect to time.

so, I = dQ/dt

so, $\frac{dQ}{dt}=3t^2+2t+5$

or, $\int\limits^Q_0=\int\limits^2_0{(3t^2+2t+5)}\,dt$

or, $Q=3\int\limits^2_0 {t^2}\,dt+2\int\limits^2_0{t}\,dt+5\int\limits^2_0dt$

or, Q = $3\left[\frac{t^3}{3}\right]^2_0+2\left[\frac{t^2}{2}\right]^2_0+5[t]^2_0$

or, Q = [2³ - 0³] + [2² - 0²] + 5[2 - 0]

or, Q = 8 + 4 + 10 = 22C

hence, charge flowing on the cross sectional of the wire in time from t = 0 to 2s is 22C.