Cells and electrical measurements
A source transfers
A cell converts chemical into electrical transferred around a circuit. Its electromotive , emf, is the supplied per unit charge by the source, measured in volts. Despite its historical name, emf is not a mechanical in newtons. Potential difference across a load measures transferred per unit charge in that part of the circuit. An ideal source maintains its stated regardless of , but a real source has losses and operating limits. The internal- model captures one important effect by representing the source as an ideal emf ε in series with r.
Terminal during discharge
For a cell supplying I through an external R, use. The terminal is. The term Ir is the internal drop during discharge. For ε = 12 V, and, is 2 A and terminal is 10 V. The ideal model predicts open-circuit approaching ε when is negligible. A voltmeter has finite , so an actual measurement can still draw a small . State the circuit condition rather than calling every measured the emf automatically.
accounting checks the model
Multiply by to obtain εI = I²R + I²r. The source's total electrical contribution is divided between useful external transfer and internal heating in this simple model. In the 12 V example, the source contributes 24 W, the external resistor receives 20 W and the internal dissipates 4 W. The external fraction is R/(R + r), under these assumptions. A large can cause significant internal heating and a lower terminal . This is a reason to analyse the model carefully, not an invitation to short-circuit a real cell.
Charging reverses the transfer
A rechargeable cell accepts electrical during charging and stores some of it chemically. In the simplest model with the entering its positive terminal, an external must provide a terminal ε + Ir. The sign differs from ordinary discharge because direction and transfer differ. Real charging is more complicated: chemistry, state of charge, temperature and control electronics affect safe operation. Primary cells are intended for non-rechargeable use, while secondary cells are designed for suitable repeated charging. That classification does not every battery can be recharged using any or procedure.
Key definition
Primary cells
Intended for non-rechargeable use , while secondary cells are designed for suitable repeated charging.
Exam keywords:intendednon-rechargeablesecondarydesigned
Combining identical cells
For n identical cells connected in series with matching polarity, total emf is nε and internal is nr. With an external load R, is nε/(R + nr). For n identical cells in a simple ideal parallel arrangement, the emf remains ε while equivalent internal is r/n. Parallel does not multiply . These results assume identical cells in compatible condition and ideal connections; mismatched real sources can exchange harmful currents. In a calculation, count polarity, trace the connections and state the identical-cell assumption. A reversed series cell subtracts rather than adds its emf.
Measure without changing it greatly
An ammeter is connected in series so it carries the branch . Its should be small relative to the circuit part being measured. An ideal ammeter has zero , but a real instrument produces some drop and has limits. Inserting an ammeter across an ideal source is not the correct measurement arrangement. A voltmeter connects in parallel across two points and should have high so it diverts little . Instrument loading means the meter can change the quantity being measured. This is especially relevant for a high- source or small .
Key definition
Instrument loading
The meter can change the quantity being measured.
Exam keywords:changequantitymeasured
A galvanometer can be adapted
A sensitive galvanometer responds to a small . To extend its range, connect a low- shunt in parallel so most bypasses the movement. At full scale, the movement and shunt have equal potential differences. Thus. For a movement with Ig = 0.001 A and extended to 1 A, S is approximately 0.1001 Ω. The shunt is small, not a large series resistor. Keeping the units and branch currents visible prevents choosing a formula only from the name of the instrument.
Extending a range
To make a voltmeter from the same movement, put a large multiplier M in series. At full scale, so. For a 5 V range, Ig = 0.001 A and, total must be 5,000 Ω and the added is 4,900 Ω. Distinguish added from total . A range switch changes the appropriate network. Real meters have calibration, tolerance and protection considerations; the simple movement model explains the principle without specifying a construction exercise.
Null methods and potentiometers
A potentiometer compares a source against the potential drop along a uniform wire carrying a steady . At balance, a detector shows zero in the comparison branch. Because the source being compared supplies no detector at null, its internal does not create the usual loading drop in that branch. If potential k is constant, emf equals kl at balance length l. For two sources under the same . The driving arrangement must support a sufficient range and the wire should remain uniform and at stable temperature for the simple relation to hold.
Bridge measurements and uncertainty
A balanced Wheatstone bridge has no detector and relates the ratios of its two arms. In a common metre-bridge arrangement with the unknown and reference on corresponding sides, the labels in the actual diagram determine which ratio is correct. Never attach the formula to a memorised left-right description without tracing the arms. A balance close to the middle usually avoids extreme length ratios. Contact , wire nonuniformity, heating and reading uncertainty affect measurements. Repeat readings and interchange suitable components in a supervised experiment to investigate systematic effects rather than assuming that repetition removes every error.
Interpreting data and practical questions
A graph of terminal V against discharge I has intercept ε and −r when the model is appropriate. If falls from 1.50 V to 1.30 V while rises from zero to 0.40 A, the inferred internal is 0.50 Ω. Read the graph's scale and intercept rather than joining units indiscriminately. Distinguish resolution, uncertainty and systematic bias in a measurement report. A result can have many displayed digits without equivalent accuracy. Good answers connect the connection diagram, limiting assumptions, numerical substitution and physical interpretation; they also identify when an ideal meter or identical-cell approximation is being used.