Electromotive Force (e.m.f.) (ε)
Definition of e.m.f.: Electromotive force (e.m.f.) is the total amount of energy that a power source, like a battery, gives to one coulomb of electric charge to make it move all the way around a complete circuit
No current condition: When there is no current flowing (nothing is moving through the wires), the e.m.f. is the same as the potential difference you would measure across the battery’s two ends.
Energy conversion: The e.m.f. tells us how much energy has been changed from other types—like chemical energy in a battery or mechanical energy in a generator—into electrical energy.
Source property: E.m.f. is a built-in property of the power source itself. It doesn’t depend on what is connected outside the source.
Unit of e.m.f.: We measure e.m.f. in volts (V), and 1 volt means 1 joule of energy is given to every 1 coulomb of charge.
Energy formula: The formula to calculate e.m.f. is ε = E/Q. Here, E is the energy in joules, and Q is the amount of charge in coulombs.
Work done meaning: E.m.f. also means the work done by the source to move one unit of positive charge from a lower electrical position to a higher one inside the source.
Internal Resistance (r)
Internal resistance definition: Internal resistance is the small amount of resistance, or opposition to the flow of electric current, that comes from inside the battery or power supply itself. Even though we think of a battery as a perfect source of electricity, it actually has some internal parts that slow down the flow of electricity slightly.
Cause of internal resistance: This internal resistance is caused by the materials and chemicals inside the battery. These include the liquid or paste called the electrolyte, and the solid metal parts called the electrodes. As the electric current passes through these materials, it faces a little resistance.
Aging effect: Over time, as a battery or power source gets older and is used again and again, the materials inside begin to wear out or change. This usually increases the internal resistance, which means the battery becomes weaker and doesn’t work as well as before.
Voltage drop: Because of the internal resistance, not all the electrical energy from the battery’s full power (its e.m.f.) reaches the rest of the circuit. Some of the energy gets used up inside the battery itself. This makes the actual voltage you can measure at the battery’s terminals lower than its e.m.f.
Efficiency impact: The internal resistance turns some of the electrical energy into heat inside the battery. This heat is wasted energy, and it means that less power is left for the rest of the circuit to use. So, the battery becomes less efficient at doing useful work.
Unit of internal resistance: We measure internal resistance using the unit called the ohm, which is written using the Greek letter omega (Ω). Just like with other types of resistance, a higher number means more opposition to current.
Terminal Potential Difference (V)
Terminal p.d. definition: Terminal potential difference is the voltage that you can actually measure at the two ends (called terminals) of a battery when it is connected in a circuit and electric current is flowing. It shows how much voltage is available to the rest of the circuit.
Difference from e.m.f.: When current is flowing through the circuit, the terminal voltage is usually a bit less than the battery’s e.m.f. This is because some of the voltage is lost inside the battery itself due to internal resistance.
Main formula: We can calculate the terminal voltage using this formula: V = ε – Ir. In this equation, V is the terminal voltage, ε (e.m.f.) is the full power of the battery, I is the current flowing in the circuit, and r is the internal resistance.
Voltage loss: The part of the formula “Ir” shows how much voltage is lost inside the battery. This lost voltage is sometimes called the “lost volts” because it’s not available to power the rest of the circuit.
Open circuit case: If the circuit is open (meaning no current is flowing), then I = 0, so Ir = 0. That means the terminal voltage becomes exactly the same as the e.m.f., because no voltage is lost inside the battery.
Relationship Between e.m.f. and Terminal Potential Difference
No current condition: When there is no current flowing in the circuit, the terminal voltage is equal to the e.m.f. We can write this as V = ε.
Current flowing condition: But if current is flowing through the circuit, some of the voltage is lost inside the battery due to internal resistance. So in this case, the terminal voltage is less than the e.m.f.
Formula rearrangement: We can rearrange the terminal voltage formula V = ε – Ir to make e.m.f. the subject: ε = V + Ir. This shows that the full e.m.f. is made up of the part that reaches the circuit (V) plus the part that is lost inside the battery (Ir).
Graph shape: If you draw a graph of terminal voltage (V) on the vertical (y) axis against current (I) on the horizontal (x) axis, you get a straight line that slopes downwards. This line shows how voltage drops as current increases.
Graph meaning: On this graph, the place where the line hits the y-axis (called the y-intercept) shows the e.m.f. of the battery. The slope (also called the gradient) of the line tells you the internal resistance r, and it is negative because the voltage goes down as current increases.
Key Differences
Definition difference: E.m.f. is the total energy given to each unit of charge by the battery or power source. Terminal voltage is the amount of that energy that actually gets delivered to the circuit for use.
Measurement condition: E.m.f. is measured when the circuit is not working (no current flowing). Terminal voltage is measured when the circuit is working (current is flowing).
Formula comparison: Both formulas show the same relationship: ε = V + Ir and V = ε – Ir. They just show it in different ways, depending on which part you want to find.
Value distinction: E.m.f. is always the same as or more than terminal voltage. It is never less, because terminal voltage loses energy inside the battery.
Influence distinction: E.m.f. depends only on the battery or power source. Terminal voltage depends on both the e.m.f. and the internal resistance inside the battery.
Determining e.m.f. and Internal Resistance Experimentally
Experimental setup: To measure the e.m.f. and internal resistance of a battery, you can build a simple circuit. You will need a battery, a variable resistor (so you can change the resistance), an ammeter (to measure current), and a voltmeter(to measure voltage across the battery).
Adjusting current: By turning the knob on the variable resistor, you can change the resistance. This changes the amount of current flowing in the circuit. For each setting, record the current from the ammeter and the voltage from the voltmeter.
Plotting graph: Now, draw a graph with voltage (V) on the vertical axis and current (I) on the horizontal axis. This will help you visualize the relationship.
Extracting values: From the graph, the point where the line hits the vertical axis is the e.m.f. of the battery. The slope of the line tells you the negative of the internal resistance. That means the value of the slope (with a negative sign) is equal to the internal resistance r.