The figure shows a network in which the cell is ideal and it has an emf E . The potential difference across the resistance 2 R is

Step-by-step solution

In the given circuit, resistors 4 R and 2 R are connected in parallel while resistance R is connected in series to it. Hence, equivalent resistance is, of parallel combination 1 R ′ = 1 4 R + 1 2 R ⇒ R ' = 8 6 R = 4 3 R ⟹ R " = R + 4 3 R = 7 R 3 (series combination) Given, emf is E volts, thereforeusing ohm's law, i = E R '' = 3 E 7 R Potential difference across R is V = i r = 3 E 7 R × R = 3 E 7 Potential difference across 2R is V ′ = E - 3 E 7 = 4 E 7