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 ($V=IR$ ) and terminal voltage formula ($V_{term} = \epsilon- Ir$ )
• Conceptual understanding and voltage divider formula ( $V_{x} = V_{total} \, \cdot \, \frac{R_{x} } {R_{total} }$ )

• 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 ($\epsilon$) and an internal resistor ($R_{int}$ or $r$ ) connected in series.


• Terminal Voltage ($V_{term}$) 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:
• $V_{term} = \epsilon- Ir$


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


• 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:
• $V_{term} = V_{used \, up} = V_{external}$
• And the $V_{total}$ or $\epsilon = V_{internal \, resistor} = V_{external \, resistor(s)}$


• 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:
• $V_{term} = V_{ext} = \epsilon \, \cdot \, \frac{R_{ext} } {R_{total} }$