Three identical cells, each of emf 2 V and internal resistance 1 , are connected in series across an unknown external resistor of resistance R . An ideal voltmeter connected across the resistor reads 4.5 V . The value of R is _____ .

Step-by-step solution

Equivalent emf of the three cells in series, E_ eq = 3 2 = 6 V . Equivalent internal resistance, r_ eq = 3 1 = 3 . Let the current in the circuit be I . Using Ohm's law for the complete circuit: I = E_ eq R + r_ eq = 6 R + 3 The ideal voltmeter reads the terminal voltage across the external resistor R . V = IR 4.5 = ( 6 R + 3 ) R Solving for R : 4.5(R + 3) = 6R 4.5R + 13.5 = 6R 1.5R = 13.5 R = 9 Answer: 9