Question

Observe the circuit R₁ = R₂ = R₃ = 200 Ω. If reading of voltmeter is 100 V, resistance of voltmeter is 1000 Ω. Find the Emf of the battery.

Answer 1

Given values are R₁ = R₂ = R₃ = 200 Ω. 

and Voltmeter reading = V = 100 V. 

Resistance of Voltmeter = R_v = 1000 Ω. 

In the given circuit R₁ and R₂ are in series 

R = R₁ + R₂ = 200 + 200 = 400 Ω 

Resultant resistance (400 Ω) and voltmeter (1000 Ω) are always in parallel.

So R_r = RR_v/R + R_v = 400 x 1000/ 1400 = 2/7 x 10³Ω

According to Ohm's law V = IR_r = I = V/R_r 

= 100 x 7/2 x 10³ = 7/20 Amp.

∴ Amount of current passing through the circuit is 7/20 Amp.

200 Ω and 2000/7 Ω are in series.

∴ Resultant resistance = R_r = 2000/7 + 200 = 3400/7 Ω

∴ V = IR_r = 2E = 7/20 x 3400/7 = 170 Volts 

[∴ Here E₁ + E₂ = E + E = 2E]

E = 170/2 = 85 Volts.