How can three resistors of resistances 2 Ω, 3 Ω and 6 Ω be connected to give a total resistance of (a) 4 Ω, (b) 1 Ω? - Science

How can three resistors of resistances 2 Ω, 3 Ω and 6 Ω be connected to give a total resistance of (a) 4 Ω, (b) 1 Ω?

Solution

There are three resistors of resistances 2 Ω, 3 Ω, and 6 Ω respectively.

(a) The following circuit diagram shows the connection of the three resistors.

H

ere, 6 Ω and 3 Ω resistors are connected in parallel.
Therefore, their equivalent resistance will be given by

1/(1/6+1/3)=(6xx3)/(6+3)=2 Ω

This equivalent resistor of resistance 2 Ω is connected to a 2 Ω resistor in series.
Therefore, the equivalent resistance of the circuit = 2 Ω + 2 Ω = 4 Ω
Hence the total resistance of the circuit is 4 Ω.

(b) The following circuit diagram shows the connection of the three resistors.

All the resistors are connected in series. Therefore, their equivalent resistance will be given as

1/(1/2+1/3+1/6)=1/((3+2+1)/6)=6/6=1Omega

Concept: System of Resistors - Resistances in Parallel
Is there an error in this question or solution?

APPEARS IN

NCERT Class 10 Science
Chapter 12 Electricity
Q 4 | Page 216