, and electric circuits
Electric is the rate of flow of electric charge. The relationship gives in amperes when charge is measured in coulombs and time in seconds. Conventional is defined in the direction a positive charge would move. In metal wires, the mobile electrons drift in the opposite direction to conventional , while the circuit as a whole transfers .
Potential difference describes transferred per unit charge. A 6 V can transfer 6 J per coulomb passing through it, subject to the actual circuit conditions. and are measured differently. Connect an ammeter in series with the component whose is required, and a voltmeter in parallel across the component whose potential difference is required.
relates potential difference to through. An ohmic conductor at constant temperature obeys with remaining constant. A filament lamp does not have a constant over a wide range because its temperature changes. Do not assume every electrical component has a straight-line – graph through the origin without considering its behaviour.
In a series arrangement, the same passes through each component and the potential difference is shared. Series resistances add. In a parallel arrangement, each branch has the same potential difference, while the total is the sum of branch currents. For two parallel resistors. The equivalent is smaller than the smallest individual branch .
Electrical can be calculated using. For an ohmic resistor, substitution also gives or P = V²/R. Electrical transferred is. Joules require in watts and time in seconds; commercial electricity units often use kilowatt-hours. One kilowatt-hour is the transferred by a 1 kW device operating for one hour, not a unit of .
Solve circuits in stages: draw the connections clearly, find an equivalent if appropriate, calculate the total , and then return to individual components. Include units and check whether each result is plausible. Never test mains circuits as a practice exercise. School circuit work should use the specified low- equipment and follow the teacher’s safety instructions, especially when changing connections or handling heated components.
Charge conservation and junctions
does not get used up by a resistor. Charge entering an ordinary circuit junction equals charge leaving when no charge accumulates there. If3 A reaches a junction and one branch carries1 A, the other carries2 A. is transferred from charges to components while charges continue moving through the circuit. A break stops steady in a simple series arrangement. Potential difference always refers to two points; ' at a wire' is incomplete without a reference. Use a consistent conventional- direction and do not add electron drift as a second independent .
, resistivity and temperature
A uniform wire has, with resistivityρ, length L and cross-sectional area A. Doubling length doubles at fixed area, material and temperature. Doubling circular-wire diameter increases area fourfold and reduces to one quarter. Resistivity is a material property in Ω m, while describes a particular object. Metallic generally increases with temperature over the ordinary school range; a thermistor can behave differently. On a V-against-I graph is R, while on I-against-V it is1/R. Inspect axis labels before interpreting the slope.
Emf and internal
Electromotive ε is supplied per charge, not a mechanical . A source supplying I with internal r has terminal . For a simple loop with external R. Lost volts Ir represent internal transfer per coulomb, not disappearing charge. With very large external , tends to zero and terminal approaches emf. A short circuit can create a large hazardous limited by internal and connection resistances, so it is not a suitable classroom trial without specialised protective apparatus.
Networks and potential dividers
Series resistors have the same and share . An unloaded potential divider gives Vout across R₂. A connected load changes the effective , so this relation cannot be applied unchanged without checking loading. Parallel branches share the same pair of nodes and equal potential difference, regardless of how far apart they are drawn. Adding a parallel path lowers equivalent and increases source if terminal remains fixed. Reduce combinations in stages and return to the original diagram to recover individual component values.
Meter arrangements and interpretation
An ideal ammeter has negligible and connects in series. An ideal voltmeter has high and connects across a component. Connecting a low- ammeter directly across a source can damage equipment. Real meters influence the circuit to some degree; choose a suitable range and inspect scale divisions. A galvanometer can become an ammeter using a low- shunt in parallel, or a voltmeter using a high series . At full-scale coil Ig and coil G, shunt for range I, and series multiplier for range V. Use the actual coil specification before calculation.
Electrical heating and protection
For constant and , heating transfer is I²Rt. A poor contact can overheat for the same -transfer reason as a designed heater, but without suitable construction. Household appliances are connected in parallel to receive the independently. A fuse or suitable circuit breaker interrupts excessive , while an earth conductor can provide a protective low- path for an exposed conductive case in the relevant installation. A residual- device responds to imbalance and has a different role. These principles do not qualify a learner to wire mains installations; practical work needs appropriate equipment and qualified supervision.
A complete network check
Suppose6 Ω and3 Ω are parallel, followed by4 Ω in series. The parallel equivalent is2 Ω and total6 Ω. An ideal12 V source supplies2 A. The4 Ω resistor has8 V across it and the parallel pair4 V. Branch currents are4/6 =0.667 A and4/3 =1.333 A, adding to2 A. Check source power12 ×2 =24 W against component powers. This separate account can expose an incorrect connection interpretation. Draw nodes and trace actual conducting paths rather than deciding series or parallel from whether components appear next to each other.
Self-check with units
A6 V cell of internal resistance1 Ω supplies5 Ω externally. Total resistance6 Ω gives current1 A and terminal voltage5 V. The cell supplies6 J per coulomb; the external resistor receives5 J per coulomb and internal accounts for1 J per coulomb. A2 A for three minutes transfers Q =It =2 ×180 =360 C. Minutes must become seconds. An calculation in joules similarly requires time in seconds when using watts. , charge, and describe distinct quantities even though the same circuit links them.