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##### Intros
###### Lessons
1. Introduction to EMF and Terminal Voltage:
2. How do we make our physics circuits more realistic?
3. What is internal resistance?
4. What does EMF stand for and how is it different from terminal voltage?
5. What are the main formulas relating to terminal voltage?
##### Examples
###### Lessons
1. Calculating Internal Resistance and Terminal Voltage using Two Methods 1. Using the traditional terminal voltage formula method:
1. Calculate the voltage used by the internal resistor of the battery.
2. Calculate the terminal voltage.
2. Using the voltage divider method:
1. Calculate the voltage used by the internal resistor of the battery.
2. Calculate the terminal voltage.
2. Calculating Internal Resistance and Terminal Voltage using Two Methods (Multiple Resistors) 1. Using the traditional terminal voltage formula method:
1. Find the terminal voltage.
2. What is the voltage used up by Rint?
2. Using the voltage divider method:
1. Find the terminal voltage.
2. What is the voltage used up by Rint?
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. 1. Using the traditional terminal voltage formula method:
1. What is the EMF?
2. If the external resistor is replaced with a resistor of 4.4$\Omega$, what is the new voltage of the battery?
2. Using the voltage divider method:
1. What is the EMF?
2. If the external resistor is replaced with a resistor of 4.4$\Omega$, what is the new voltage of the battery?
###### Topic Notes

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 ( $V_{x} = V_{total} \, \cdot \, \frac{R_{x} } {R_{total} }$ )

Notes:

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