GATE EC 2015 Set 3 — Question 65
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Electromagnetics → Maxwell's Equations
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Question
A coaxial capacitor of inner radius and outer radius has a capacitance per unit length of . If the ratio of outer radius to inner radius is doubled, the capacitance per unit length (in ) is ______.
Correct answer
120 to 120.4
Solution
The capacitance per unit length of a coaxial capacitor is given by the formula:
where is the outer radius and is the inner radius.Step 1: Use initial conditions to find the constant factor.
Given when the ratio .
Step 2: Calculate the new capacitance.
The ratio of outer radius to inner radius is doubled, so the new ratio .
The new capacitance is:
Step 3: Relate to .
.
where is the outer radius and is the inner radius.Step 1: Use initial conditions to find the constant factor.
Given when the ratio .
Step 2: Calculate the new capacitance.
The ratio of outer radius to inner radius is doubled, so the new ratio .
The new capacitance is:
Step 3: Relate to .
.
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