Question 246: Current Electricity

Question

A current through a wire depends on time as i = $$\alpha$$0t + $$\beta$$t2where $$\alpha$$0 = 20 A/s and $$\beta$$ = 8 As$$-$$2. Find the charge crossed through a section of the wire in 15 s.

Accepted Answer

Given, $$i = {\alpha _0}t + \beta {t^2}$$
where, $$\alpha$$
0
= 20 A/s, $$\beta$$ = 8 A/s
2
We know that, $$i = {{dq} \over {dt}}$$
$$ \Rightarrow {{dq} \over {dt}} = i = {\alpha _0}t + \beta {t^2} = 20t + 8{t^2}$$
$$ \Rightarrow dq = (20t + 8{t^2})dt$$
On integrating both sides, we get
$$\int\limits_0^q {dq = \int\limits_0^{15} {(2t + 8{t^2})dt} } $$
$$q = \left[ {{{20{t^2}} \over 2} + {{8{t^3}} \over 3}} ight]_0^{15} = 10 	imes {(15)^2} + {8 \over 3} 	imes {(15)^3}$$
$$	herefore$$ q = 11250 C

Answer

2250 C

Answer

2100 C

Answer

260 C

Answer

11250 C

Current Electricity

A current through a wire depends on time as i = $\alpha0t + \betat2where \alpha0 = 20 A/s and \beta = 8 As-$2. Find the charge crossed through a section of the wire in 15 s.

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