Product of equivalent resistances

Electricity and Magnetism Level 1

Circuit: 1

Circuit: 2

Circuit: 3

Circuit: 4

In all the above circuits, there are three resistors each of resistance $1 \Omega$ . Let $R_{eq_1}$ , $R_{eq_2}$ , $R_{eq_3}$ and $R_{eq_4}$ be the equivalent resistances of the circuit $1$ , $2$ , $3$ and $4$ respectively. Find $R_{eq_1} \times R_{eq_2} \times R_{eq_3} \times R_{eq_4}$

The answer is 1.

1 solution

Jaime Cabrera
Mar 5, 2016

For C1, $R_{eq1}=1+1+1=3$ For C2, $\frac { 1 }{ R_{ eq2 } } =\frac { 1 }{ 1+1 } +1=\frac { 3 }{ 2 } \therefore { R }_{ eq2 }=\frac { 2 }{ 3 }$ For C3, $\frac { 1 }{ R_{ eq3 } } =1+1+1=3 \therefore { R }_{ eq3 }=\frac { 1 }{ 3 }$ For C4, $R_{ eq4 } =\frac { 1 }{ 1+1 } +1=\frac { 3 }{ 2 }$ Finally, we obtain the product $3\times\frac{2}{3}\times\frac{1}{3}\times\frac{3}{2}=\boxed{1}$

Product of equivalent resistances

The answer is 1.

1 solution

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