Question 628: Current Electricity

Question

The charge flowing through a resistance R varies with time t is Q = at $$-$$ bt
2
, where $$a$$ and $$b$$ are positive constants. The total heat produced in R is

Accepted Answer

Given: Charge Q = at Ã¢ÂÂ bt
2
$$ 	herefore $$ Current $$i = {{\partial Q} \over {\partial t}} = a - 2bt$$
$$\left\{ {for\,i = 0 \Rightarrow t = {a \over {2b}}} ight\}$$
From joule's law of heating, heat produced
dH = i
2
Rdt
$$H = \int\limits_0^{a/2b} {{{\left( {a - 2bt} ight)}^2}Rdt} $$
$$H = \left. {{{{{\left( {a - 2bt} ight)}^2}R} \over { - 3 	imes 2b}}} ight|_0^{{a \over {2b}}} = {{{a^3}R} \over {6b}}$$

Answer

$${{{a^3}R} \over {2b}}$$

Answer

$${{{a^3}R} \over {b}}$$

Answer

$${{{a^3}R} \over {6b}}$$

Answer

$${{{a^3}R} \over {3b}}$$

Current Electricity

The charge flowing through a resistance R varies with time t is Q = at $- bt 2 , where a and b$ are positive constants. The total heat produced in R is

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