Electrical Units and Resistance Calculations

Current, potential difference and resistance

An electronic system needs suitable resistor values to control the current through its components. Three electrical quantities help you choose those values.

Current is the rate at which electric charge flows through a circuit. Its symbol is $I$, and it is measured in amperes, written A and often called amps. Current flows through a component.

Potential difference, also called voltage, is the energy transferred per unit of charge between two points. Its symbol is $V$, and it is measured in volts, also written V. A supply provides a potential difference that drives current around a complete circuit; a component has a potential difference across it.

Resistance describes how strongly a component opposes current. Its symbol is $R$, and it is measured in ohms, written Ω. At the same potential difference, increasing resistance reduces current; decreasing resistance increases current.

Using Ohm’s law

For a resistor whose temperature remains constant, current increases in proportion to the potential difference across it. The relationship between potential difference, current and resistance is:

$$V = I \times R$$

You can rearrange this equation according to the quantity you need:

$$I = \frac{V}{R} \qquad R = \frac{V}{I}$$

Use the potential difference across the resistor and the current through that same resistor. With current in amperes and resistance in ohms, the calculated potential difference is in volts.

For example, suppose a resistor has a resistance of 300 Ω and carries a current of 0.02 A. Its potential difference is $V = 0.02 \times 300 = 6\text{ V}$. This means that 6 V is required across that resistor to produce a current of 0.02 A, or 20 mA.

The same relationship works in reverse. If you know the potential difference is 6 V and the resistance is 300 Ω, then $I = 6 / 300 = 0.02\text{ A}$. If you instead know the potential difference is 6 V and the current is 0.02 A, then $R = 6 / 0.02 = 300\text{ Ω}$.

Resistors in series: one path

Resistors are connected in series when current passes through them one after another along a single path. The same current flows through every resistor, while the supply potential difference is shared between them.

Each resistor adds opposition to the flow of charge, so their resistances add:

$$R_{\text{total}} = R_1 + R_2 + R_3 + \cdots$$

The subscripts simply distinguish the individual resistors. Include every resistor in the series path.

Suppose you connect a 60 Ω resistor and two 120 Ω resistors in series. Their total resistance is $60 + 120 + 120 = 300\text{ Ω}$. The combination behaves like a single 300 Ω resistor. Adding another series resistor would increase the total resistance and, with the supply voltage unchanged, reduce the current.

If a design needs a particular resistance, you can also use subtraction to find a missing value. For example, a series combination totalling 300 Ω, with known resistors of 60 Ω and 120 Ω, needs a third resistor of $300 - 60 - 120 = 120\text{ Ω}$.

Resistors in parallel: separate paths

Resistors are connected in parallel when each is connected between the same two points. Current can divide between the branches, and every resistor has the same potential difference across it.

Adding a parallel branch provides an extra route for charge. More current can flow overall at the same supply voltage, so the total resistance decreases. It is smaller than the smallest individual resistor in the parallel combination.

For parallel resistors, add the reciprocals of their resistances:

$$\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \cdots$$

A reciprocal means one divided by a number. After adding the reciprocals, take the reciprocal again to obtain the total resistance.

For the same 60 Ω, 120 Ω and 120 Ω resistors, now connected in parallel:

$$\frac{1}{R_{\text{total}}} = \frac{1}{60} + \frac{1}{120} + \frac{1}{120} = \frac{4}{120} = \frac{1}{30}$$

Therefore, $R_{\text{total}} = 30\text{ Ω}$. The same three components give 300 Ω in series but only 30 Ω in parallel: the connection changes their overall effect. Once you have found the total resistance, you can use $I = V/R_{\text{total}}$ to calculate the total current drawn from a supply.

Quantities and units

• Current: $I$, amperes (A), through a component.
• Potential difference: , volts (V), across a component.