5.2 How to do calculations involving a series circuit

Using some basic rules and Ohm's Law (V = IR) I'll show you how to work out all sorts of things from just only the three pieces of data give.

(a) The total resistance of the two resistors in series (2.0 Ω and 6.0 Ω)

When resistance are wired in series, you add them up to get the total resistance.

R_total = R₁ + R₂ = 6.0 + 2.0 = 8.0 Ω (ohms)

 

(b) The current flowing in the circuit

We know the total p.d. (V_total) across the resistors part of the circuit and we know the total resistance.

V_total = 12.0 V  (marked on power supply) and  R_total = 8.0 Ω (calculated in (a)).

Also, in a series circuit, the current is the same at any point in the circuit.

So, using Ohm's Law: V = IR, so I = V_total/R_total = 12.0/8.0 = 1.5 A (amps)

Therefore readings:   I₁ = I₂ = I₃ = 1.5 A

 

(c) We can now calculate the p.d across each resistor using Ohm's Law V = IR

V₁ = 1.5 x 6.0 = 9.0 V   and   V₂ = 1.5 x 2.0 = 3.0 V

Noting the total p.d. of the circuit is shared between the various components of the system,

AND the p.d. across a resistor is proportional to the resistance value,

(check out ... 6 Ω and 9 V for resistor 1, similarly 2 Ω and 3 V for resistor 2)

so, bigger the resistance, the greater the potential difference across it,

 

AND the p.d. values for components wired in series add up to the maximum source p.d.

(which is 12.0 V here)

So for the p.d., V_total = V₁ + V₂ = 12.0 = 9.0 + 3.0  (which gives you a check on the previous calculation!)

 

When two or more resistances are wired in series they all have to share the total p.d. of the circuit.

The higher the value of the resistance, the bigger its share of the total source p.d. in other words the p.d. is always shared between resistances/components wired in series.

The p.d. across each resistor must be lower than V_total, BUT, the current is still the same around all points of the circuit.

However, as you increase the number of resistances in the series, the current is reduced (I = V/R).

 

If you carry out the experiment, the readings should match in principle the theoretical values above.

If you don't know the value of a resistance, using the above type of circuit, you can measure the current lowing through it and the p.d. across it and then use Ohm's Law R = V/I to calculate it.

 

See also Part 3.1

Ohm's Law, investigations of resistance, I-V graphs and calculations using I = V/R

and also Part 5.7

Extra QUESTIONS on series and parallel circuits with worked out ANSWERS