Two resistors R₁ = 6 , and R₂ = 12 , are connected in series across an ideal 12 V battery. A non-ideal voltmeter is first connected across R₁ and it reads 3 V . If the same voltmeter is now disconnected from R₁ and connected across R₂ , its reading will be _____ V .

Step-by-step solution

Let the resistance of the voltmeter be R_v . Case 1: Voltmeter across R₁ The voltage across R₁ is 3 V . The remaining voltage from the 12 V battery drops across R₂ : V_ R2 = 12 - 3 = 9 V The current through R₂ (which is the total current) is: I = 9 12 = 0.75 A The equivalent resistance of the parallel combination of R₁ and R_v is: R_ p1 = 3 V 0.75 A = 4 , Thus, 6 R_v 6 + R_v = 4 6 R_v = 24 + 4 R_v 2 R_v = 24 R_v = 12 , Case 2: Voltmeter across R₂ The voltmeter is now in parallel with R₂ . The new equivalent resista