Question 710: Current Electricity

Question

When two identical batteries of internal resistance 1 $$\Omega$$ each are connected in series across a resistor R, the rate of heat produced in R is J
1
. When the same batteries are connected in parallel across R, the rate is J
2
. If J
1
= 2.25 J
2
, then the value of R in $$\Omega$$ is __________.

Accepted Answer

In series : When the batteries are connected in series, we have
$${J_1} = {\left( {{{2E} \over {R + 2}}} ight)^2}R$$
In parallel : When the batteries are connected in parallel, we have
$${J_2} = {\left( {{E \over {R + (1/2)}}} ight)^2}R$$
It is given that,
$${{{J_1}} \over {{J_2}}} = 2.25$$
$$ \Rightarrow {4 \over {{{(R + 2)}^2}}} 	imes {{{{(2R + 1)}^2}} \over 4} = 2.25 \Rightarrow {{2R + 1} \over {R + 2}} = 1.5$$
$$ \Rightarrow 2R + 1 = 1.5R + 3 \Rightarrow 0.5R = 2$$
Therefore, $$R = 4\Omega $$.

Current Electricity

When two identical batteries of internal resistance 1 $\Omega each are connected in series across a resistor R, the rate of heat produced in R is J 1 . When the same batteries are connected in parallel across R, the rate is J 2 . If J 1 = 2.25 J 2 , then the value of R in \Omega$ is __________.

Integer / Numeric Answer Type