In the circuit shown in the Figure, cell is ideal and R₂=100 . A voltmeter of internal resistance 200 reads V₁₂=4 ~V and V ₂₃=6 ~V between the pair of points 1-2 and 2-3 respectively. What will be the reading of the voltmeter between the points 1-3.(mark the anser in V )

Step-by-step solution

Let emf of the cell be E . Current through the voltmeter (when connected between 1-2) is V₁₂ R_V = 4 2 0 0 = 1 5 0 A Current through R₁= 4 R₁ Current through R₂= 4 R₁ + 1 50 Potential difference across R₂= ( 4 R₁ + 1 50 ) 100= 400 R₁ +2 E=4+ ( 400 R₁ +2 )=6+ 400 R₁ When the voltmeter is connected between 2-3 Current through voltmeter = 6 200 A Current through R_ 2 = 6 1 0 0 A Current through aligned & R₁= 6 200 + 6 100 = 18 200 = 9 100 A & E= 9 R₁ 100 +6 aligned From (1) and (2) 9 R₁ 100 +6=6+ 400 R₁ R₁= 40000 9 =