Chapter 6, Problem 6.1P

To determine

The equivalent resistance $R_e$ of the circuit where all the resistances are same as resistance R.

Answer to Problem 6.1P

The equivalent resistance is $R_e=\frac{8R}{5}$.

Explanation of Solution

Given information:

The given relation between the voltage and current is,

$v_s=R_{e}i$

All resistors are same having the value equivalent to R.

Concept Used:

$R_e$ is simplified using the concept of series and parallel circuit.

Calculation:

Mark the points in the given circuit to simplify the calculations.

Resistance between the point 1 & 2 is a series and parallel combination so, $R\Vert R+R=\frac{3R}{2}$. Now resistance between point 3 & 4 is in parallel with the resistance between the point 1&2 so, $\frac{3R}{2}\Vert R=\frac{3R}{5}$.

Now resistance R is connected in series with the resistance between the points 3 and 4. So, total equivalent resistance is $\frac{3R}{5}+R=\frac{8R}{5}$.

Conclusion:

The equivalent resistance R_e is given as $\frac{8R}{5}$.