Potential difference and resistance at constant current

A potential difference across a conductor drives an electric current through it. The conductor’s resistance opposes that current. To maintain the same current through a greater resistance, a greater potential difference is needed.

The relationship between potential difference, current and resistance is:

Here, $$V$$ is the potential difference in volts ($$\mathrm{V}$$), $$I$$ is the current in amperes ($$\mathrm{A}$$), and $$R$$ is the resistance in ohms ($$\Omega$$).

Keeping the current constant

When current is constant, potential difference is directly proportional to resistance. For example, doubling the resistance doubles the potential difference needed to maintain the same current.

If the current is $$2,\mathrm{A}$$ and the resistance is $$3,\Omega$$, the potential difference is $$V = 2 \times 3 = 6,\mathrm{V}$$. If the resistance doubles to $$6,\Omega$$ while the current remains $$2,\mathrm{A}$$, the required potential difference also doubles to $$12,\mathrm{V}$$.

Potential dividers

A potential divider uses resistors in series to share a supply potential difference. The same current flows through each resistor. Since the potential difference across a resistor is the current multiplied by its resistance, the resistor with the larger resistance has the larger potential difference across it.

For two resistors with resistances $$R_1$$ and $$R_2$$ and corresponding potential differences $$V_1$$ and $$V_2$$:

The potential differences across the resistors add to the supply potential difference: $$V_1 + V_2 = V_{\text{supply}}$$. Combining this with the resistance ratio gives:

For example, if $$R_1 = 2,\text{k}\Omega$$ and $$R_2 = 4,\text{k}\Omega$$, the resistances are in the ratio $$1:2$$. With a $$12,\text{V}$$ supply, the potential differences are also in the ratio $$1:2$$: $$V_1 = 4,\text{V}$$ and $$V_2 = 8,\text{V}$$.

Variable potential divider

A variable potential divider has a resistive track connected across the supply and a movable contact on the track. The contact divides the track into two sections. Taking the output between the contact and one end gives the potential difference across the section between those two points.

Moving the contact changes the relative resistances of the two sections, so it changes the fraction of the supply potential difference taken as the output. Moving the contact towards the chosen end decreases the resistance of that section and reduces the output potential difference; moving it away increases both.

These relationships apply when negligible current is drawn from the output. Under that condition, essentially the same current flows through both sections of the track.