EMF and terminal voltage - Electric Circuits

EMF and terminal voltage



In this lesson, we will learn:

  • How to compare and contrast the circuits we’ve been drawing so far (an ideal circuit) with a more realistic circuit (containing an EMF as well as internal resistance).
  • What is EMF (Electromotive Force)? And what is terminal voltage?
  • How to solve for terminal voltage and EMF using 2 methods:
    • The traditional formulas for Ohm’s Law (V=IRV=IR ) and terminal voltage formula (Vterm=ϵIrV_{term} = \epsilon- Ir )
    • Conceptual understanding and voltage divider formula ( Vx=VtotalRxRtotal V_{x} = V_{total} \, \cdot \, \frac{R_{x} } {R_{total} } )


  • To represent a more realistic electric circuit, a battery actually contains internal resistance—in other words, the battery itself uses up some of the voltage that it provides to the whole circuit.
    • Internal resistance is unavoidable because any material has some resistance
    • Metals have a very low (but not zero) resistance and are good conductors for electricity; the greater the resistance of a material, the worse its conductivity

  • EMF stands for Electromotive Force. It is a device that transforms one type of energy into electrical energy. (i.e. An alkaline battery undergoes redox reactions whereby chemical energy is transformed into electrical energy to power the circuit).

  • A battery is considered a source of electromotive force. A battery is actually composed of an EMF (ϵ \epsilon) and an internal resistor (RintR_{int} or rr ) connected in series.

  • Terminal Voltage (VtermV_{term}) is the voltage (potential difference) measured between the terminals (positive and negative terminals) of a battery.
    • When no current is flowing through the circuit: emf = terminal voltage
    • When there is current flowing through the circuit: emf > terminal voltage

  • The general formula for the Terminal Voltage is given as:
    • Vterm=ϵIrV_{term} = \epsilon- Ir

  • Where:
    • VtermV_{term} is the voltage between the terminals of the battery (in volts, V)
    • ϵ \epsilon is the EMF of the battery; total/maximum voltage (in volts, V)
    • II is the total current flowing through the circuit (in amperes, A)
    • rr is the internal resistance within the battery (in Ohms; Ω \Omega )
    • IrIr is actually the voltage drop across the internal resistor (V=IRV = IR), thus the formula can be adjusted: Vterm=ϵVr V_{term} = \epsilon - V_{r}

  • Furthermore, the terminal voltage represents the amount of electric potential energy (voltage) that is available to the circuit outside of (external to) the battery itself. Thus:
    • Vterm=Vusedup=Vexternal V_{term} = V_{used \, up} = V_{external}
    • And the Vtotal V_{total} or ϵ=Vinternalresistor=Vexternalresistor(s) \epsilon = V_{internal \, resistor} = V_{external \, resistor(s)}

  • To modify the voltage divider general formula to be used with EMF and terminal voltage questions, we can solve for the total external voltage drop:
    • Vterm=Vext=ϵRextRtotal V_{term} = V_{ext} = \epsilon \, \cdot \, \frac{R_{ext} } {R_{total} }
  • Intro Lesson
    Introduction to EMF and Terminal Voltage:
  • 1.
    Calculating Internal Resistance and Terminal Voltage using Two Methods

    EMF Terminal Voltage
  • 2.
    Calculating Internal Resistance and Terminal Voltage using Two Methods (Multiple Resistors)

    EMF Terminal Voltage
  • 3.
    Solving for EMF using Two Methods
    The battery is measured from terminal to terminal and observed to have an electric potential difference of 6.25V.

    EMF Terminal Voltage
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EMF and terminal voltage

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