Resistors in parallel

A parallel circuit gives the current more than one path. The current splits between the branches, and the branch currents add up to the total. The rule for the equivalent resistance uses reciprocals: 1/Rp = 1/R1 + 1/R2 + 1/R3.

So Rp is smaller than the smallest single resistor. Homes wire their appliances in parallel. Each one gets the full voltage and can be switched on or off by itself.

A small example

A 6 Ω and a 3 Ω resistor are joined in parallel to a 6 V battery.

• 1/Rp = 1/(6 Ω) + 1/(3 Ω) = 1/(6 Ω) + 2/(6 Ω) = 3/(6 Ω).
• Rp = 2 Ω.
• I = V/Rp = 6 V / 2 Ω = 3 A.
• Check: 6 V / 6 Ω = 1 A and 6 V / 3 Ω = 2 A. 1 A + 2 A = 3 A.

A last step is easy to miss: 1/Rp is not Rp. Turn the fraction over.

Where marks go

Question 37 of CBSE's 2026-27 Science sample paper mixes parallel and series parts with a 15 V battery. The 2026-27 Science marking scheme works in steps. Two parallel pairs become 1 Ω and 1.5 Ω. These join 5 Ω in series to give 7.5 Ω, so I = 2 A. That part carries 2 marks. The voltage between A and B, 2 V, carries 1 more.

Show each reduced circuit as a line of working. Read how resistors in series add, and how step marking works.

About the author

Deepti Sardana

Founder Member & Academic Lead

An IIT alumna (M.Sc., M.Phil.) with over 25 years in teaching, child psychology and learning assessment. As Academic Lead at EduBrahma, she leads the method TRUtesting uses to find where and why a child loses marks.

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