Question

Three resistors are connected across a cell with an internal resistance of r and an emf of 1.8 V in the given circuit diagram. Determine the internal resistance r and the current flowing through the three resistors.

Answer 1

Given:

emf of cell, E = 1.8 V

Total current, I = 0.3 A

Resistors 3 Ω and 1.5 Ω are connected in parallel.

Their equivalent resistance is in series with 4 Ω.

1. Calculate the equivalent resistance of the parallel combination:

`1/R = 1/3 + 1/1.5`

`1/R = 1/3 + 2/3`

`1/R 3/3`

`1/R = 1`

R = 1 Ω

2. Calculate the external resistance:

`R_"external"`​ = 1 + 4 = 5 Ω

3. Calculate the total resistance of the circuit:

Using Ohm's law,

`R_"total"​ = E/I`

​= `1.8/0.3`

= 6 Ω

4. Calculate the internal resistance:

r = `R_"total" - R_"external"`​

= 6 − 5

= 1 Ω

5. Calculate the current through the three resistors:

Voltage across the parallel combination:

V = I × R

= 0.3 × 1

= 0.3 V

Current through 3 Ω resistor:

I = `0.3/3` = 0.1 A

Current through 1.5 Ω resistor:

I = `0.3/1.5` = 0.2 A

Current through 4 Ω resistor (series):

I = 0.3 A