Ohm’s Law: MDCAT Physics notes
Ohm’s Law MDCAT notes: V = IR, ohmic and non-ohmic devices, I-V graph slope, series and parallel resistors, electrical power, potentiometer and divider.
Ohm's law
The current through a metallic conductor is directly proportional to the potential difference across it, provided its temperature and physical state remain constant:
$$V = IR$$
$R$ is the resistance, measured in ohms ($\Omega$), 1 $\Omega$ = 1 V A$^{-1}$. Resistance is a property of the conductor: doubling $V$ doubles $I$ but leaves $R$ unchanged.
I-V graphs
- For an ohmic conductor the graph of $I$ against $V$ is a straight line through the origin (linear relation).
- Slope of $I$–$V$ graph $= 1/R$: a steeper line means a lower resistance.
- Slope of a $V$–$I$ graph $= R$.
| Ohmic (obey Ohm's law) | Non-ohmic (curved I-V graph) |
|---|---|
| Metallic wires (copper) at constant temperature, carbon resistors | Diode, transistor, filament lamp, thermistor, vacuum tube |
A filament bulb is non-ohmic because its temperature, and so its resistance, rises as the current increases. A diode conducts in one direction only.
Resistors in series and parallel
| Series | Parallel |
|---|---|
| Same current through each | Same voltage across each |
| $R_e = R_1 + R_2 + \dots$ | $\frac{1}{R_e} = \frac{1}{R_1} + \frac{1}{R_2} + \dots$ |
| $R_e$ larger than the largest | $R_e$ smaller than the smallest |
- $n$ equal resistors $R$ in parallel give $R/n$.
- Two in parallel: current divides inversely: $I_1 = I\frac{R_2}{R_1+R_2}$. Example: 10 A into 2 $\Omega$ and 3 $\Omega$ in parallel gives 6 A and 4 A.
- A wire of resistance $R$ bent into a ring: between ends of a diameter, two halves $R/2$ in parallel give $R/4$.
- Household lamps are in parallel, so switching on more lamps decreases total resistance.
- In series, if both resistors have the same percentage tolerance, the combination has that same percentage tolerance.
- A closed switch (ideal) has zero resistance, so zero potential drop.
Electrical power
$$P = VI = I^2R = \frac{V^2}{R}$$
- Volt × ampere = watt.
- At fixed $R$, doubling $V$ gives four times the power.
- Bulbs rated for the same voltage: $R = V^2/P$, so a 60 W bulb has twice the resistance of a 120 W bulb.
- Energy $W = Pt$; in kWh use kW × hours. Example: 4 A through 25 $\Omega$ for 5 h: $P = 400$ W, energy = 2 kWh.
Kirchhoff's rules
Junction rule: conservation of charge. Loop rule: conservation of energy. They were framed for steady (DC) circuits; the Wheatstone bridge is an application.
Potential divider and potentiometer
- A potential divider gives a continuously variable potential from a fixed supply.
- A potentiometer compares or measures emfs by a null method, drawing no current at balance. It is more accurate than a voltmeter but bulky and not portable.
- A longer slide wire gives a smaller potential gradient, so higher sensitivity and accuracy.
An ohmmeter (in a multimeter) needs an internal battery to drive current through the unknown resistor. A galvanometer is an electromechanical device.
Key formulas
- $V = IR$
- $R_s = \sum R_i$; $1/R_p = \sum 1/R_i$
- $P = VI = I^2R = V^2/R$
Common MDCAT traps
- Ohm's law requires constant temperature.
- High slope on an $I$–$V$ graph means low resistance.
- Current divides so that the smaller resistance carries the larger current.
- Filament bulb and diode are non-ohmic.
- Lower-wattage bulb has the higher resistance.
Quick revision
- Series: same current; parallel: same voltage.
- Resistance does not change with applied voltage.
- Power $\propto V^2$ at constant $R$.
- Potentiometer sensitivity improves with a longer wire.