Question

The batteries in FIGURE P27.68 are identical. Both resistors have equal currents. What is the resistance of the resistor on the right?

Short answer

The resistance of the resistor on the right is $2R$.

Step-by-step solution

Given Information

The batteries in the given picture are identical. Then both resistors have equal currents.

Step 2:Explanation

Let the current in both resistance is $\text{'}i\text{'}$.

For Resistance $R$,

$i=\frac{E}{R}$(1)

Voltage across unknown resistor$=2E$

So,$i=\frac{2E}{R_{unknown}}$(2)

Substitute (1) and (2)

$\frac{E}{R}=\frac{2E}{R_{unknown}}$

$\Rightarrow R_{unknown}=2R$

Therefore, the resistance of the resistor on the right is$2R$