Current, potential difference and resistance flashcards

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Electric current
The rate of flow of charged particles (rate of flow of charge). Unit: ampere, A.
The coulomb
The charge passing a point when a current of 1 A flows for 1 s: 1 C = 1 A s.
Potential difference
The energy transferred per unit charge between two points. Unit: volt, 1 V = 1 J C⁻¹.
Resistance
R = V/I: the p.d. across a component divided by the current in it. Unit: ohm, 1 Ω = 1 V A⁻¹.
Ohm's law
For a metallic conductor at constant temperature, the current is directly proportional to the p.d. across it.
Ohmic conductor
A component whose resistance stays constant as the current changes: its I–V graph is a straight line through the origin.
Drift velocity
The small average velocity of charge carriers along a conductor, superimposed on their random motion, when a p.d. is applied.
Number density of charge carriers, n
The number of free charge carriers per unit volume (unit m⁻³).
Conventional current
Current drawn from + to − round the external circuit: the direction positive charge would flow. Electrons in metals drift the opposite way.
Current and charge
I = ΔQ/Δt (Yes)
Potential difference, energy and charge
V = W/Q (Yes)
Definition of resistance
R = V/I (Yes)
Electrical power and energy
P = VI and W = VIt (Yes)
Power in terms of resistance (two forms)
P = I²R and P = V²/R (Yes)
Current in terms of drift velocity
I = nqvA (Yes)
Number of electrons in a charge Q
N = Q/e, with e = 1.60 × 10⁻¹⁹ C. (No — learn it)
Area under a current–time graph
The charge that has passed.
I–V graph of an ohmic conductor
A straight line through the origin; resistance = V/I is the same at every point.
Resistance from a curved I–V graph
R = V/I using the coordinates of the point — not the gradient of the tangent.
Shape of a P–V graph for a fixed resistor
A parabola through the origin (P = V²/R); a smaller R gives a steeper curve.
Where do the ammeter and voltmeter go?
Ammeter in series with the component; voltmeter in parallel across it.
Is current used up in a lamp?
No. Charge is conserved, so current in = current out. Energy is transferred from the charge carriers to the lamp.
Why does a lamp light at once although the drift velocity is tiny?
The electric field is set up round the circuit almost instantly, so free electrons everywhere start drifting together.
Why do electrons drift faster in a thinner part of a series circuit?
Same I, n and q, so v ∝ 1/A: smaller area, larger drift velocity.
Why do metals have a much lower resistivity than semiconductors and insulators?
Metals have a huge n (~10²⁸–10²⁹ m⁻³); with fewer carriers, a given current needs a much larger drift velocity and so a much larger p.d.
Why is Ohm's law only a special case of R = V/I?
R = V/I defines resistance for any component; Ohm's law adds that R stays constant (metal at constant temperature).
Same p.d., two resistors: which dissipates more power?
The smaller resistance, because P = V²/R.
A current of 0.60 A flows for 15 min. Charge, and number of electrons?
Q = 0.60 × 900 = 540 C; N = 540 ÷ 1.60 × 10⁻¹⁹ = 3.4 × 10²¹.
25 C passes through a 9.0 V battery-powered toy. Energy transferred?
W = QV = 25 × 9.0 = 225 J (2.3 × 10² J).
A 1200 W hair dryer runs on 230 V. Current and resistance?
I = P/V = 5.2 A; R = V²/P = 44 Ω.
A 47 Ω resistor carries 0.30 A. Power dissipated?
P = I²R = 0.30² × 47 = 4.2 W.
A 60 W lamp is on 5 hours a day for 30 days. Energy in kWh?
0.060 kW × 150 h = 9.0 kWh (3.2 × 10⁷ J).
3.0 A in a copper wire of area 2.5 mm², n = 8.5 × 10²⁸ m⁻³. Drift velocity?
v = I/(nqA) = 3.0 ÷ (8.5 × 10²⁸ × 1.60 × 10⁻¹⁹ × 2.5 × 10⁻⁶) = 8.8 × 10⁻⁵ m s⁻¹.
Stating Ohm's law
Include ‘metallic conductor’, ‘constant temperature’ and ‘directly proportional’. V = IR alone is not the law.
Converting mm² to m²
× 10⁻⁶ (1 mm = 10⁻³ m, squared). Halve a diameter before squaring.
Which V goes into P = V²/R?
The p.d. across that same component — e.g. for a cable, IR across the cable, not the supply p.d.
Current in a fixed resistor rises by 50%: percentage increase in power?
Find the factor first (e.g. 1.5² = 2.25), then subtract 1: a 125% increase.

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