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Question

Shown in the figure is a semicircular metallic strip that has thickness t and resistivity ρ . Its inner radius is R1 and outer radius is R2 . If a voltage V0 is applied across its two ends, a current I flows in it. The value of current I is given by :



A
I=V0tπρln(R1R2)
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B
I=V0tπρln(R2R1)
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C
I=V0R1R2πρtln(R1R2)
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D
I=πV0tρln(R1R2)
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Solution

The correct option is B I=V0tπρln(R2R1)
Let us choose an elementary ring at a distance x from the centre and having thickness dx

Now ,

All such elements are in parallel

1dr=R2R1tdxρπx

1r=tπρln(R2R1)

Resistance =πρtln(R2R1)

Current
I=V0tln(R2R1)πρ

So , the option (b) is correct .


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