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Question
Two resistors P and Q of the same material and length but of different thickness are connected in parallel to a battery. The cross- sectional area of P is twice that of Q. What is the ratio of
(a) The resistance of P to the resistance of Q?
(b) The current in P to the current in Q?
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Solution
We know that, R = ρ `1/"a"`
(a) Given length of resistors P and Q made of same material is same (say= 1)
Let 'a' be the area of cross-section of Q.
Then, the area of cross-section of Pis '2a'.
`"R"_"P"/"R"_"Q" = [ρ (1/[2"a"])]/[ρ (1/"a")] = 1/2`
the required ratio is 1: 2.
(b) AJC to ohm's law,
V=IR
If resistors P and Q are connected across the same voltage supply V, then
`"I"_"P"/"I"_"Q" = "R"_"g"/"R"_"p" = 2/1`
:. the required ratio of current in P to current in Qi s 2: 1.
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