# Answers to Problems - Internal Resistance

1. A 9 V battery is connected in series with a load and the terminal voltage is found to be 8 V. Current through the circuit is measured as 5 A. What is the internal resistance of the battery?

 RINTERNAL  = ℰ  -  VTERMINAL = 9 V  -  8 V =  0.2 Ω I 5 A

2. What is the EMF of the battery in the following circuit?

 REXTERNAL  = 12 Ω × 4 Ω =  3 Ω 12 Ω + 4 Ω

=  I  ×  (REXTERNAL  +  RINTERNAL)  =  5A  ×  13Ω  =  65V

3. What is the internal resistance of the battery in the following circuit?

 REXTERNAL  = 6 Ω × 10 Ω =  3.75 Ω 6 Ω + 10 Ω

VEXTERNAL  =  I  ×  REXTERNAL  =  1.5 A  ×  3.75 Ω  =   5.625 V

VINTERNAL  =    -  VEXTERNAL  =  6 V  -  5.625 V  =  0.375 V

 RINTERNAL  = VINTERNAL = 0.375 V =  0.25 Ω I 1.5 A

4. A battery has an internal resistance of 0.5 Ω and an EMF of 1.5 V. When connected in series to a load resistance, the terminal voltage falls to 1.45 V. What current is flowing in the circuit, and what is the value of the load resistance?

VINTERNAL  =    -  VEXTERNAL  =  1.5 V  -  1.45 V  =   0.05 V

 I  = VINTERNAL = 0.05 V =  0.1 A RINTERNAL 0.5 Ω

 RLOAD  = VEXTERNAL = 1.45 V =  14.5 Ω I 0.1 A

5. What is the terminal voltage for a battery with an EMF of 12 V and an internal resistance of 0.5 Ω when it is connected in series with to a 10 Ω resistor?

 I  = ℰ = 12 V =  1.143 A RINTERNAL  +  REXTERNAL 10.5 Ω

VEXTERNAL  =  REXTERNAL  ×  I  =  10 Ω  ×  1.143 A  =  11.43 V