Question

A cell of emf E and internal resistance r is connected to two external resistance R₁ and R₂ and a perfect ammeter. The current in the circuit is measured in four different situations:

(i) without any external resistance in the circuit

(ii) with resistance R₁ only

(iii) with R₁ and R₂ in series combination

(iv) with R₁ and R₂ in parallel combination

The currents measured in the four cases are 0.42 A, 1.05 A, 1.4 A and 4.2 A, but not necessarily in the order. Identify the currents corresponding to the four cases mentioned above.

Answer 1

The current relating to corresponding situations are as follows:

(i) Without any external resistance in the circuit −

`I_1 = E/r`

The current in this case would be maximum, so I₁ = 4.2A

(ii) With resistance R₁ only −

`I_2 = E/(r + R_1)`

The current in this case will be the second smallest value, so I₂ = 1.05 A

(iii) With R₁ and R₂ in series combination −

`I_3 = E/(r+ (R_1+R_2))`

The current in this case will be minimum as the resistance will be maximum, so I = 0.42 A.

(iv) With R₁ and R₂ in parallel combination-

`I_4 = E/(r +((R_1R_2)/(R_1 +R_1)))`

The current in this case would be the second largest value, so I = 1.4 A.