Question

The current in a wire varies with time according to the equation I = 4 +2 t, where I is in ampere and t is in second. The quantity of charge which has to be passed through a cross-section of the wire during the time t = 2 s to t = 6 s is

• A. 40 C
• B. 48 C
• C. 38 C
• D. 43 C

Answer 1

Answer: (B)

48 C

Answer 2

: Let dq be the charge which passes in a small interval of time dt. Then

dq = Idt

or dq = (4+2t)dt

On integrating, we get,

$\mathrm { q } = \int _ { 2 } ^ { 6 } ( 4 + 2 \mathrm { t } ) \mathrm { dt } = \left[ 4 \mathrm { t } + \mathrm { t } ^ { 2 } \right] _ { 2 } ^ { 6 } = 48 \mathrm { C }$