Action and use of circuit components
Section: Electricity & Magnetism | Syllabus: Cambridge AS Level Physics 9702
Voltage and Resistance Relationship For a constant current through a circuit, the p.d. across a conductor increases as its resistance increases . From Ohm's Law V = IR If I is constant and R increases, then V must increase.
This principle is used in potential dividers to produce different output voltages. The Potential Divider A potential divider (or voltage divider) is a circuit that produces an output voltage that is a fraction of the input voltage.
FIG 4.3.10: Potential divider circuit Circuit showing input voltage Vin across two resistors R₁ and R₂ in series. Output voltage Vout is measured across R₂. The circuit effectively "divides" the input voltage between the two resistors.
R_1/R_2 = V_1/V_2 The ratio of resistances equals the ratio of p.d.s across them. Key Principle The larger resistance gets the larger share of the voltage. Variable Potential Divider A variable potential divider uses a variable resistor (or potentiometer) to give a continuously adjustable output voltage.
FIG 4.3.11: Variable potential divider Three-terminal potentiometer: input voltage connected across both ends. A sliding contact (wiper) moves along the resistor. Output voltage is taken between one end and the wiper.
Moving the wiper changes the output voltage from 0 to Vin. Applications Volume controls – adjust audio signal level Dimmer switches – control lamp brightness Sensor circuits – with thermistor or LDR to detect temperature/light changes Sensor Circuits with Potential Dividers Temperature Sensor (Thermistor) A thermistor in series with a fixed resistor: When cold : thermistor has high R → larger share of voltage across thermistor When hot : thermistor has low R → smaller share of voltage across thermistor Light Sensor (LDR) An LDR in series with a fixed resistor: In dark : LDR has high R → larger share of voltage across LDR In bright light : LDR has low R → smaller share of voltage across LDR Worked Example Example: Potential Divider Calculation Question: A 6 V supply is connected across two resistors: R₁ = 4 Ω and R₂ = 2 Ω in series.
Calculate the p.d. across each resistor. Answer Using the ratio: V_1/V_2 = R_1/R_2 = 4/2 = 2 So V_1 = 2V_2 Also: V_1 + V_2 = 6 V Substituting: 2V_2 + V_2 = 6, so 3V_2 = 6 V_2 = 2 V (across 2 Ω resistor) V_1 = 4 V (across 4 Ω resistor)
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