How do you combine resistors is series and parallel?

In a series circuit each resistor will have the same current passing through it.  If we assume that the wires connecting the resistors have no resistance, then the total potential difference, V, is given by Kirchhoff’s Voltage Law;

V=V1+V2+V3+…

Using Ohm’s Law,

V=IR,

we get

IR=IR1+IR2+IR3+…

as the current is the same in each resistor we can cancel them out to get;

R=R1+R2+R3+…

Basically if you have 2 or more resistors in series the total resistance is simply the sum of each resistance.

Combining resistances in parallel is a bit more complicated; in a parallel circuit each resistor will have the same potential difference, but the current flowing through them will not necessarily be the same.  If we start with the conservation of charge we get;

I=I1+I2+I3+…

using Ohm’s Law again gives us

V/R=V/R1+V/R2+V/R3+…

and as V is the same for all the resistors we get

1/R=1/R1+1/R2+1/R3+…

If you have 2 or more resistors in parallel the reciprocal of the resistance (1 over the resistance) is the sum of the reciprocals of each resistance.

Answered by Matt Q. Physics tutor

3238 Views

See similar Physics A Level tutors

Related Physics A Level answers

All answers ▸

What is the minimum frequency of electromagnetic radiation needed for a photon to ionise an atom of sodium? ( An atom of sodium has an ionisation energy of 5.15 eV.)


A 1kg spring has an unloaded length 10cm and has an elastic constant of 100N/m. It is compressed to 6cm then placed facing upwards on the floor. When released it travels vertically upwards. How high does it jump? You may assume no energy is lost to heat o


What is the photoelectric effect and how does it provide evidence for the quantisation of electromagnetic radiation?


What is dimensional analysis and how is it used?


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2024

Terms & Conditions|Privacy Policy
Cookie Preferences