Question 363: Current Electricity

Question

An electric current is passed through a circuit containing two wires of the same material, connected in parallel. If the lengths and radii are in the ratio of  $${4 \over 3}$$ and $${2 \over 3}$$, then the ratio of the current passing through the wires will be

Accepted Answer

$${i_1}{R_1} = {i_2}{R_2}\,\,\,\,\,\,\,\,\,\,$$ (same potential difference)
V = I
1
R
1
= I
1
$$ 	imes $$$${{ho {l_1}} \over {\pi r_1^2}}$$
Also V = I
2
R
2
= I
2
$$ 	imes $$$${{ho {l_2}} \over {\pi r_2^2}}$$
$$ 	herefore $$ I
1
$$ 	imes $$$${{ho {l_1}} \over {\pi r_1^2}}$$ = I
2
$$ 	imes $$$${{ho {l_2}} \over {\pi r_2^2}}$$
$$ \Rightarrow $$ $${{{I_1}} \over {{I_2}}} = {{{\ell _1}} \over {{\ell _2}}} 	imes {{r_1^2} \over {r_2^2}}$$
$$ = {3 \over 4} 	imes {4 \over 9} = {1 \over 3}\,\,$$

Answer

$$8/9$$

Answer

$$1/3$$

Answer

$$3$$

Answer

$$2$$

Current Electricity

An electric current is passed through a circuit containing two wires of the same material, connected in parallel. If the lengths and radii are in the ratio of ${4 \over 3} and {2 \over 3}$, then the ratio of the current passing through the wires will be

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