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CBSE Class 10 Answered

establish the Formula of equivalent resistance for the parallel combination of three resistance
Asked by sarthaksinghrajput6 | 31 Jan, 2022, 08:12: PM
answered-by-expert Expert Answer

Suppose if three resistances are connected in a parallel combination across a power source of voltage V and current I

Now as we can see from the circuit diagram below, the total current flowing through resistance R1, R2, R3 are I1, I2 and I3 respectively.

i.e., I equals I subscript 1 plus I subscript 2 plus I subscript 3

Whereas voltage drop across all three-resistances connected in parallel will be same.

 V equals space I R space rightwards double arrow I equals V divided by R space space space space
therefore V divided by R subscript e equals V divided by R subscript 1 plus V divided by R subscript 2 plus V divided by R subscript 3
1 divided by R subscript e equals 1 divided by R subscript 1 plus 1 divided by R subscript 2 plus 1 divided by R subscript 3

This is the expression for effective resistance offered by resistance connected in parallel combination.

We can use this for ‘n’ number of resistance as well and the expression for than will be as shown below.

 1 divided by R subscript e equals 1 divided by R subscript 1 plus 1 divided by R subscript 2 horizontal ellipsis.. plus 1 divided by R subscript n

Here, Re is effective resistance of parallel combination and n is number of resistances connected in parallel combination.

Answered by Jayesh Sah | 01 Feb, 2022, 12:33: AM
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