Electromotive Force & Resistor
Shared 5/18/2026•5 views
### Electromotive Force (EMF) and Terminal Voltage - **Electromotive Force (EMF), $\mathcal{E}$:** - The maximum potential difference across the terminals of a cell when no current is drawn from it (open circuit). - It's the energy supplied by the cell per unit charge to drive current through the entire circuit (internal and external). - Unit: Volt (V). - **Terminal Voltage (V):** - The potential difference across the terminals of a cell when current is being drawn from it (closed circuit). - Due to internal resistance, terminal voltage is always less than EMF when current flows. - Unit: Volt (V). - **Relationship:** $V = \mathcal{E} - Ir$ - Where: - $V$ = Terminal voltage - $\mathcal{E}$ = EMF - $I$ = Current flowing through the circuit - $r$ = Internal resistance of the cell ### Internal Resistance of a Cell ($r$) - **Definition:** The opposition offered by the electrolyte and electrodes of a cell to the flow of current through it. - **Factors affecting internal resistance:** 1. **Nature of electrolyte:** Higher conductivity, lower resistance. 2. **Concentration of electrolyte:** Higher concentration, lower resistance (up to a certain limit). 3. **Distance between electrodes:** Greater distance, higher resistance. 4. **Area of electrodes immersed in electrolyte:** Larger area, lower resistance. 5. **Temperature:** Higher temperature, lower resistance. - **Formula:** $r = (\frac{\mathcal{E}}{V} - 1)R$ or $r = \frac{\mathcal{E} - V}{I}$ - Where $R$ is the external resistance in the circuit. - **Power dissipated internally:** $P_{internal} = I^2 r$ ### Combination of Resistors: Series - **Arrangement:** Resistors are connected end-to-end, so the same current flows through each resistor. - **Equivalent Resistance ($R_S$):** The sum of individual resistances. - $R_S = R_1 + R_2 + R_3 + ... + R_n$ - **Characteristics:** - **Current:** Same through all resistors ($I_1 = I_2 = I_3 = I$). - **Voltage:** Divides across resistors ($V = V_1 + V_2 + V_3$). - **Use:** To increase the total resistance in a circuit. ### Combination of Resistors: Parallel - **Arrangement:** Resistors are connected between two common points, so the potential difference across each resistor is the same. - **Equivalent Resistance ($R_P$):** The reciprocal of the equivalent resistance is the sum of the reciprocals of individual resistances. - $\frac{1}{R_P} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + ... + \frac{1}{R_n}$ - For two resistors: $R_P = \frac{R_1 R_2}{R_1 + R_2}$ - **Characteristics:** - **Current:** Divides among resistors ($I = I_1 + I_2 + I_3$). - **Voltage:** Same across all resistors ($V_1 = V_2 = V_3 = V$). - **Use:** To decrease the total resistance in a circuit and provide multiple paths for current. ### Ohm's Law - **Statement:** The current flowing through a conductor is directly proportional to the potential difference across its ends, provided its physical conditions (like temperature) remain unchanged. - **Formula:** $V = IR$ - Where: - $V$ = Potential difference (Volts) - $I$ = Current (Amperes) - $R$ = Resistance (Ohms) - **Application to a circuit with internal resistance:** - Total resistance in the circuit = External Resistance ($R$) + Internal Resistance ($r$) = $R+r$ - Total current ($I$) drawn from the cell: $I = \frac{\mathcal{E}}{R+r}$
