In a network as shown in the figure the potential difference across the resistance 2R is (the cell has an emf of E and has no internal resistance):

Options

A. `2E`
B. `(2E)/(7)`
C. `(E)/(7)`
D. `E`

Answer

B

Explanation

Equivalent resistance for the given circuit is

`(1)/(R')=(1)/(4R)+(1)/(2R)=(6R)/(8R^(2))`
`R'=(8)/(6)R=(4)/(3)R rArr R''=R+(4)/(3)R = (7R)/(3)`
Given, emf is E volts, therefore, `i=(E )/(R )=(3E)/(7R)`
Potential difference across R is V `= ir=(3R)/(7R)xx R = (3E)/(7)`
Potential difference across 2R is V' `= E-(3E)/(7)=(4E)/(7)`