Ohm’s Law

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Provided that temperature does not vary, the ratio of p.d. across the ends of a conductor to the current flowing in the conductor is a constant. This relationship is known as Ohm’s Law and it leads to the relationship:

V / I = a constant = R

where V is the potential difference (or voltage drop) in Volts (V), I is the current in Amperes (A), and R is the resistance in Ohms (see Fig. below).  The formula may be arranged to make V, I or R the subject, as follows:

V = I × R , I = V / R and  R = V / I 

The triangle shown in Fig. A should help you remember these three important relationships. However, it’s worth noting that, when performing calculations of currents, voltages and resistances in practical circuits it is seldom necessary to work with an accuracy of better than ±1% simply because component tolerances are usually greater than this. Furthermore, in calculations involving Ohm’s Law, it can sometimes be convenient to work in units of k< and mA (or M< and µA) in which case potential differences will be expressed directly in V.

 

Example 

A 12 Ohm resistor is connected to a 6V battery. What current will flow in the resistor?

Solution

Here we must use  I = V / R (where V = 6 V and  R = 12 Ohm):

I = V / R = 6 V / 12 Ohm = 0.5 A (or 500 mA)

Hence a current of 500 mA will flow in the resistor.

Example

A current of 100 mA flows in a 56 Ohm resistor. What voltage drop (potential difference) will be developed across the resistor?

Solution

Here we must use  V = I × R and ensure that we work in units of Volts (V), Amperes (A) and Ohms.

V = I × R = 0.1 A × 56 Ohm = 5.6 V

(Note that 100 mA is the same as 0.1 A.) This calculation shows that a p.d. of 5.6 V will be developed across the resistor.

Example

A voltage drop of 15 V appears across a resistor in which a current of 1 mA flows. What is the value of the resistance?

Solution

R = V / I = 15 V / 0.001 A = 15,000 < = 15 kOhm

Note that it is often more convenient to work in units of mA and V which will produce an answer directly in kOhm, i.e.

R = V / I = 15 V/ l mA = 15 kOhm