The potentiometer
Section: D.C. Circuits | Syllabus: Cambridge AS Level Physics 9702
The Potentiometer A potentiometer is a device used to measure or compare potential differences with high accuracy. It works on the principle of a potential divider but uses a continuous wire instead of discrete resistors.
Potentiometer An instrument that compares an unknown p.d. or e.m.f. with a known p.d. by finding the position along a uniform wire where no current flows through a galvanometer (null point). Construction A slide-wire potentiometer consists of: A uniform resistance wire (typically 1 metre long) stretched along a metre rule A driver cell (battery) providing a known p.d.
across the full length of the wire A sliding contact (jockey) that can touch any point along the wire A galvanometer to detect current flow The source whose e.m.f. is to be measured FIG 10.19: Slide-Wire Potentiometer Circuit Show a circuit with: A driver cell connected across a uniform wire XZ (marked with a metre scale).
Point X at one end, Z at the other. A sliding contact (jockey) at point Y along the wire. The unknown e.m.f. (cell being tested) connected with its positive terminal to X. A galvanometer (G) connected between the negative terminal of the test cell and the jockey.
Label the length l = XY and show that both positive terminals connect to the same point X. Principle of Operation The wire acts as a continuous potential divider. If the wire has uniform cross-sectional area and resistivity, its resistance is proportional to its length: R l (for uniform wire) Therefore, for a constant current through the wire, the p.d.
across any section is proportional to its length: V l Balancing the Potentiometer The jockey is moved along the wire until the galvanometer shows zero deflection (the null point). At this point: The p.d.
across length XY of the wire equals the unknown e.m.f. No current flows through the galvanometer or the cell being tested The unknown e.m.f. is "balanced" against the p.d. across XY Balance Condition At the null point: _unknown = fraction × V_driver where l = balance length (XY), L = total wire length (XZ), V_driver = p.d.
across the whole wire Since V l along a uniform wire with constant current: _unknownV_driver = fraction The Galvanometer Galvanometer A sensitive current-detecting instrument that can measure very small currents and indicate their direction.
It has a centre-zero scale, with the pointer deflecting left or right depending on current direction. Use in Null Methods In a potentiometer, the galvanometer is used as a null detector - we only need to know when the current through it is zero, not the actual value of any current.
Advantages of using a galvanometer in null methods: The galvanometer does not need to be calibrated Only needs to detect zero current, not measure it Very small currents can be detected Direction of deflection indicates which way to move the jockey Null Methods and Their Advantages Null Method A measurement technique in which the quantity being measured is compared against a standard, and the measurement is made when a detector shows zero (null) reading.
Why Null Methods Give More Accurate Measurements When the potentiometer is balanced (galvanometer reads zero): No current flows through the cell being tested Therefore there is no p.d. drop across its internal resistance The measured value equals the true e.m.f., not the terminal p.d.
No current flows through the galvanometer The galvanometer's resistance does not affect the measurement Eliminates systematic errors from the measuring instrument Key Advantage A voltmeter always draws some current from the circuit it measures, so it measures terminal p.d.
rather than true e.m.f. A potentiometer at balance draws zero current, so it measures the true e.m.f. This makes it more accurate than a voltmeter for measuring e.m.f. Comparing Two E.m.f.s A potentiometer can compare two unknown e.m.f.s by finding the balance length for each: Comparing E.m.f.s fraction = fraction where l_1 and l_2 are the balance lengths for e.m.f.s _1 and _2 respectively This ratio method eliminates the need to know the p.d.
across the driver cell or the resistance per unit length of the wire. Worked Example: Comparing E.m.f.s Problem: A standard cell of e.m.f. 1.018 V balances at 50.9 cm on a potentiometer wire. An unknown cell balances at 75.2 cm.
What is the e.m.f. of the unknown cell? Solution: _unknown_standard = l_unknownl_standard _unknown1.018 = fraction _unknown = 1.018 × fraction = 1.018 × 1.477 _unknown = 1.50 V Worked Example: Direct E.m.f.
Measurement Problem: A potentiometer wire XZ is 1.00 m long. The variable resistor is adjusted so that there is a p.d. of 1.50 V across the full length of the wire. The galvanometer reads zero when the movable contact is positioned 47.6 cm from point X.
What is the e.m.f. of the cell being tested? Solution: Since p.d. is proportional to length along a uniform wire: fraction = fraction = fraction × V_wire = fraction × 1.50 = 0.476 × 1.50 = 0.714 V Ideal Properties of Measuring Instruments The limita…
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