10.12-10.14 - Resistance and circuit rules

Resistance and current control

Resistance describes how strongly a component opposes the flow of charge. At a fixed potential difference, a larger resistance gives a smaller current, while a smaller resistance gives a larger current. This is a change in how much charge passes each second, not a claim that current is a substance moving more slowly.

A variable resistor lets a person change resistance in a circuit. Moving its slider or turning its control changes the length of resistive material included in the conducting route. When it is connected in series with another component:

• increasing the variable resistance increases the circuit's resistance and decreases the current;
• decreasing the variable resistance decreases the circuit's resistance and increases the current.

The control does not adjust itself like a sensor. The user deliberately sets it to change or limit the current.

Potential difference $V$, current $I$ and resistance $R$ are connected by:

For a component, the potential difference must be measured across it and the current must be the current through it. The resistance can then be found by rearranging:

Worked example

A resistor has a potential difference of $6.0\text{ V}$ across it and a current of $250\text{ mA}$ through it. Calculate its resistance.

Convert the current to amperes before substitution:

Then rearrange and substitute:

The result is reported to two significant figures, matching the potential difference. A sense-check using $V = IR$ gives $0.250 \times 24 = 6.0\text{ V}$, so the value is consistent.

At the same $6.0\text{ V}$, doubling the resistance from $12\ \Omega$ to $24\ \Omega$ changes the current from $0.50\text{ A}$ to $0.25\text{ A}$. The potential difference is fixed, so greater resistance means less charge passes per second.