Find the equivalent resistance

Electricity and Magnetism Level 1

What is the equivalent resistance between A and B?

3 7 R \frac{3}{7}R 1 4 R \frac{1}{4}R 5 3 R \frac{5}{3}R R R None of these. 1 2 R \frac{1}{2}R

Md Mehedi Hasan by Md Mehedi Hasan , 22, Bangladesh

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1 solution

Md Mehedi Hasan
Oct 31, 2017

If we simplify this circuit, we find

Here the voltage difference between C C and D D is 0 0 . So in C D CD current doesn't flow. Therefore, we can neglect the C D CD line's resistance.

Now, we get the equivalent resistance,

R p = ( ( R + R ) − 1 + ( R + R ) − 1 ) − 1 = ( 1 2 R + 1 2 R ) − 1 = ( 1 R ) − 1 = R R_p={ \left( { \left( R+R \right) }^{ -1 }+{ \left( R+R \right) }^{ -1 } \right) }^{ -1 }={ \left( \frac { 1 }{ 2R } +\frac { 1 }{ 2R } \right) }^{ -1 }={ \left( \frac { 1 }{ R } \right) }^{ -1 }=\boxed { R }

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