Electromotive force and Potential difference

# Electromotive force and Potential difference ## Emf and pd, Use of meters in electric circuits, how they are connected and reasons ### Introduction Welcome to this lesson on Electromotive Force (emf) and Potential Difference (pd)! These are fundamental concepts in understanding how electric circuits work. We will also learn about the essential instruments used to measure current and voltage in a circuit: ammeters and voltmeters, and why they are connected in specific ways. ### Key Concepts #### Electromotive Force (emf) * **Definition:** Electromotive force (emf) is the energy supplied by a source (like a battery or generator) per unit charge to drive charge around a complete circuit. It is the "push" that causes current to flow. * **Units:** The unit of emf is the Volt (V), which is equivalent to Joules per Coulomb (J/C). * **Formula:** \( \text{emf} = \frac{\text{Energy (E)}}{\text{Charge (Q)}} \) * **Sources of emf:** * **Batteries:** Convert chemical energy into electrical energy. * **Generators:** Convert mechanical energy into electrical energy. * **Solar Cells:** Convert light energy into electrical energy. #### Potential Difference (pd) * **Definition:** Potential difference (pd), also known as voltage, is the work done or energy dissipated per unit charge as charge moves between two points in an electric circuit. It represents the "energy loss" as current flows through a component (e.g., a resistor, bulb). * **Units:** The unit of pd is also the Volt (V), equivalent to Joules per Coulomb (J/C). * **Formula:** \( V = \frac{\text{Work Done (W)}}{\text{Charge (Q)}} \) * **Relationship between emf and pd:** * emf is the *total* energy provided by the source. * pd is the energy *dissipated* by components in the external circuit. * In an ideal circuit (with no internal resistance), the emf of the source is equal to the total potential difference across the external circuit components. #### Internal Resistance of a Cell (r) * **Definition:** All real sources of emf (like batteries) have some internal resistance. This is the resistance offered by the electrolyte and electrodes within the cell itself to the flow of charge. * **Effects:** * When current `\( I \)` flows through the cell, some voltage is "lost" due to this internal resistance. This lost voltage is `\( Ir \)`. * The **terminal potential difference** (the actual voltage available across the terminals of the cell) is less than the emf when current is drawn from the cell. * **Formula:** \( \text{emf} (\varepsilon) = V + Ir \) where \( V \) is the terminal potential difference and \( Ir \) represents the lost volts. * Therefore, \( V = \varepsilon - Ir \). #### Measuring Devices: Ammeters and Voltmeters ##### Ammeter * **Purpose:** Measures the electric current flowing through a specific point in a circuit. * **Connection:** Always connected in **series** with the component or part of the circuit where the current is to be measured. * **Reason for series connection:** To measure the total current passing through that point, the ammeter must allow all the current to flow through it. If it were connected in parallel, it would divert current, and not measure the correct flow through the component. * **Internal Resistance:** Ammeters have a very **low internal resistance** to ensure they do not significantly impede the flow of current in the circuit and thus do not alter the current they are measuring. * **Circuit Symbol:** A circle with the letter 'A' inside. ##### Voltmeter * **Purpose:** Measures the potential difference (voltage) across two points in a circuit, typically across a component. * **Connection:** Always connected in **parallel** with the component whose potential difference is to be measured. * **Reason for parallel connection:** To measure the potential difference *between* two points, the voltmeter needs to be placed across those points. If it were connected in series, it would block the current flow due to its high resistance. * **Internal Resistance:** Voltmeters have a very **high internal resistance** to ensure that they draw negligible current from the main circuit. This way, they do not significantly alter the potential difference they are measuring or the overall circuit behavior. * **Circuit Symbol:** A circle with the letter 'V' inside. ### Vocabulary * **Electromotive Force (emf):** The total energy supplied by a source per unit charge to drive charge around a complete circuit. * **Potential Difference (pd) / Voltage:** The work done or energy dissipated per unit charge as charge moves between two points in an electric circuit. * **Volt (V):** The SI unit for both emf and potential difference. * **Ampere (A):** The SI unit for electric current. * **Ammeter:** An instrument used to measure electric current. * **Voltmeter:** An instrument used to measure potential difference. * **Internal Resistance (r):** The resistance offered by the source of emf itself. * **Terminal Potential Difference:** The actual voltage available across the terminals of a cell or power supply when current is being drawn from it. * **Lost Volts:** The voltage drop within the source itself due to its internal resistance `\( (Ir) \)`. * **Series Connection:** Components connected end-to-end, so the same current flows through each. * **Parallel Connection:** Components connected across the same two points, so the same potential difference exists across each. ### Examples #### Example 1: Calculating emf and pd A battery supplies 120 J of energy to move 10 C of charge through a circuit. **a) What is the emf of the battery?** \( \text{emf} = \frac{\text{Energy}}{\text{Charge}} = \frac{120 \text{ J}}{10 \text{ C}} = 12 \text{ V} \) **b) If 30 J of energy is dissipated across a resistor in the circuit by the same 10 C of charge, what is the potential difference across the resistor?** \( V = \frac{\text{Work Done}}{\text{Charge}} = \frac{30 \text{ J}}{10 \text{ C}} = 3 \text{ V} \) #### Example 2: Correct Meter Connection Consider a simple circuit with a battery, a resistor, and a switch. To measure the current flowing through the resistor and the voltage across it: * An **ammeter** must be placed in **series** with the resistor. * A **voltmeter** must be placed in **parallel** across the resistor. ```mermaid circuitDiagram battery "12V" b1 resistor "R" r1 ammeter a1 voltmeter v1 wire w1 from b1.p to a1.p wire w2 from a1.n to r1.p wire w3 from r1.n to b1.n wire w4 from r1.p to v1.p wire w5 from r1.n to v1.n ``` (Note: The mermaid diagram is a visualization. In actual markdown notes, you would describe this or use an image if supported.) #### Example 3: Terminal Potential Difference A dry cell has an emf of 1.5 V and an internal resistance of 0.5 \( \Omega \). If it supplies a current of 0.2 A to an external circuit, what is the terminal potential difference across the cell? Using the formula: \( V = \varepsilon - Ir \) \( V = 1.5 \text{ V} - (0.2 \text{ A} \times 0.5 \text{ }\Omega) \) \( V = 1.5 \text{ V} - 0.1 \text{ V} \) \( V = 1.4 \text{ V} \) The terminal potential difference is 1.4 V. ### Exercises 1. Define electromotive force (emf) and state its SI unit. 2. What is the main difference between emf and potential difference (pd)? 3. Why is an ammeter connected in series in a circuit? 4. Why does a voltmeter have a high internal resistance? 5. A circuit component dissipates 45 J of energy when 5 C of charge passes through it. What is the potential difference across the component? a) 50 V b) 9 V c) 0.11 V d) 225 V 6. Draw a circuit diagram showing a battery, a lamp, an ammeter measuring current through the lamp, and a voltmeter measuring voltage across the lamp. ### Assignment 1. Explain the concept of "lost volts" in a real battery. How does internal resistance affect the terminal potential difference of a power source? 2. A battery has an emf of 6 V and an internal resistance of 1.0 \( \Omega \). It is connected to an external resistor of 5.0 \( \Omega \). a) Calculate the total resistance of the circuit. b) Calculate the current flowing through the circuit. c) Calculate the potential difference across the external resistor. d) Calculate the lost volts within the battery. e) Verify that \( \varepsilon = V + Ir \). 3. Discuss the consequences of connecting a voltmeter in series and an ammeter in parallel in a simple circuit. What would happen in each case? ### Summary In this lesson, we distinguished between Electromotive Force (emf), the total energy supplied by a source, and Potential Difference (pd), the energy dissipated across a component. We learned that the units for both are Volts. We also understood the crucial role of ammeters and voltmeters in measuring current and voltage, respectively. Ammeters are connected in series due to their low resistance, while voltmeters are connected in parallel due to their high resistance. Finally, we explored the concept of internal resistance and its effect on the terminal potential difference of a power source. Mastering these concepts is vital for further study in electricity and circuit analysis.