The current flowing through a wire depends on time as I=3t2+2t +5. The charge flowing through the cross section of the wire in time from t = 0 to t = 2 sec. is

Question

The current flowing through a wire depends on time as I=3t2+2t +5. The charge flowing through the cross section of the wire in time from t = 0 to t = 2 sec. is (A) 22 C (B) 20 C (C) 18 C (D) 5 C

Tardigrade Admin · Accepted Answer

Charge Q =∫ limits02(3 t2+2 t+5) d t =[t3+t2+5 t]02 =8+4+10=22 C

Q. The current flowing through a wire depends on time as $I = 3 t^{2} + 2 t + 5.$ The charge flowing through the cross section of the wire in time from $t = 0$ to $t = 2$ sec. is

22 C

20 C

18 C

5 C

Charge $Q = 0 \int 2 (3 t^{2} + 2 t + 5) d t$
$= [t^{3} + t^{2} + 5 t]_{0}^{2}$
$= 8 + 4 + 10 = 22 C$

Q. The current flowing through a wire depends on time as I=3t2+2t+5. The charge flowing through the cross section of the wire in time from t=0 to t=2 sec. is

22 C

20 C

18 C

5 C

Charge Q=0∫2​(3t2+2t+5)dt =[t3+t2+5t]02​ =8+4+10=22C

Q. The current flowing through a wire depends on time as $I = 3 t^{2} + 2 t + 5.$ The charge flowing through the cross section of the wire in time from $t = 0$ to $t = 2$ sec. is

Charge $Q = 0 \int 2 (3 t^{2} + 2 t + 5) d t$
$= [t^{3} + t^{2} + 5 t]_{0}^{2}$
$= 8 + 4 + 10 = 22 C$