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  =    -  VTERMINAL  =  9 V  -  8 V  =  0.2 Ω
    I5 A

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

    What is the EMF of the battery in this 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?

    What is the internal resistance of the battery in this 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
    I1.5 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
    RINTERNAL0.5 Ω

    RLOAD  =  VEXTERNAL  =  1.45 V  =  14.5 Ω
    I0.1 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  =    =  12 V  =  1.143 A
    RINTERNAL  +  REXTERNAL10.5 Ω

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