Ohm's Law and Resistor Combinations
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flagWhat you'll discover
- arrow_forwardState Ohm's law and the conditions under which it holds
- arrow_forwardTake a set of V and I readings and plot the V-I graph
- arrow_forwardExplain why the slope of the V-I graph is the reciprocal of the resistance
- arrow_forwardCompute the equivalent resistance in series (R = R1 + R2) and parallel (1/R = 1/R1 + 1/R2)
- arrow_forwardExplain why current is the same in series and voltage is the same in parallel
Ohm's law
Ohm's law says that, at constant temperature, the current through a conductor is directly proportional to the potential difference across it: V = IR, with V in volts, I in amperes and R in ohms.
That is why the V-I graph of a metal wire at a steady temperature is a straight line through the origin. Its slope is ΔI/ΔV, which is 1/R, so the resistance is the reciprocal of the slope. A steeper line means a smaller resistance.
The law fails when the temperature changes — a filament lamp heats up, its resistance rises, and the V-I graph bends.
Series and parallel
In series the same current passes through every resistor, and the voltages add: R = R1 + R2 + … . Adding a resistor in series always increases the total resistance and reduces the current.
In parallel the voltage across every branch is the same, and the currents add: 1/R = 1/R1 + 1/R2 + … . Adding a branch in parallel always decreases the total resistance, because there is one more path for the charge.
Two resistors of 10 Ω and 20 Ω give 30 Ω in series but only 6.7 Ω in parallel — a fact worth checking against the readouts here.
Doing the practical properly
Connect the cell, key, rheostat, ammeter in series and voltmeter in parallel with the resistor. The ammeter must be in series because it has a very low resistance, and the voltmeter in parallel because it has a very high resistance; swapping them gives a wrong reading and can damage the meter.
Take at least five readings across the range, tabulate V and I, and plot V on the x-axis against I on the y-axis. Draw the best straight line, take two points far apart on the line (not two data points) for the slope, and compute R = 1/slope. State the temperature condition and mention that the wire heats up if the current is kept on too long.