Resistor X has length L and area of cross section A. Resistor Y has length 2L and area of cross section A/2. What is the ratio of resistances of resistor X to resistor Y if both are made of same material?
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Resistor X has length L and area of cross section A. Resistor Y has length 2L and area of cross section A/2. What is the ratio of resistances of resistor X to resistor Y if both are made of same material?
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Answer:
1:4
Explanation:
As both of the resistors are made up of the same material, their resistivity will be same.
CASE 1 [For X]:
We know that:
R= ρL /A
=> X = ρL /A ---------- Equation 1
CASE 2 [For Y]:
We know that:
R= ρL /A
=> Y= ρL' /A'
=> Y= ρ2L/[A /2]
=> Y= 4 [ρL /A] -------- Equation 2
On dividing Equation 1 by 2:
X /Y = [ρL/A] /[4(ρL /A)]
=> X /Y = 1 /4
=> X:Y = 1:4
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