Question

You have two batteries, both with an emf of 1.5V. The internal resistance of the first battery is 0.5 Ohm, and the internal resistance of the second battery is 1 Ohm.

What will be the current through an external resistor with a resistance of 2 Ohm, if the two batteries are connected in series?

What will be the current through an external resistor with a resistance of 2 Ohm, if the two batteries are connected in parallel?

What will be the current through an external resistor with a resistance of 0.25 Ohm, if the two batteries are connected in series?

What will be the current through an external resistor with a resistance of 0.25 Ohm, if the two batteries are connected in parallel?

Answer 1

(a) When the two batteries are connected in series.

Total emf = 1.5 V + 1.5 V = 3.0 V

Total resistance of the circuit = r1 + r2(internal resistance) + R (external resistance) = 0.5 + 1.0 + 2.0 = 3.5 ohm

So, current through the external resistance = Emf / Resistance

= 3.0 / 3.5 = 0.86 A

(b) When the two batteries are connected in parallel -

Total emf = 1.5 V

Total resistance of the circuit = (r1 x r2) / (r1+r2) (internal resistance) + R (external resistance) = (0.5x1.0) / (0.5+1.0) + 2.0

= 0.33 + 2.0

= 2.33 ohm

So, current through the external resistance = Emf / Resistance

= 1.5 / 2.33 = 0.64 A

(c) External resistance, R = 0.25 ohm

Total emf = 1.5 V + 1.5 V = 3.0 V

Total resistance of the circuit = r1 + r2(internal resistance) + R (external resistance) = 0.5 + 1.0 + 0.25 = 1.75 ohm

So, current through the external resistance = Emf / Resistance

= 3.0 / 1.75 = 1.71 A

(d) When the two batteries are connected in parallel -

Total emf = 1.5 V

Total resistance of the circuit = (r1 x r2) / (r1+r2) (internal resistance) + R (external resistance) = (0.5x1.0) / (0.5+1.0) + 0.25

= 0.33 + 0.25

= 0.58 ohm

So, current through the external resistance = Emf / Resistance

= 1.5 / 0.58 = 2.59 A