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Question
A piece of wire having a resistance R is cut into five equal parts.
- How will the resistance of each part of the wire change compared with the original resistance?
- If the five parts of the wire are placed in parallel, how will the resistance of the combination change?
- What will be ratio of the effective resistance in series connection to that of the parallel connection?
Solution
- Consider a piece of wire having resistance R. It cut into 5 equal parts. So number of equal resistros are 5. n = 5
When ‘n’ resistors of equal resistance R are connected in series, the equivalent resistance is ‘nR’
RS = nR
⇒ RS = 5R
⇒ R = \(\frac{\mathrm{R}_{\mathrm{s}}}{5}\)
⇒ R = 0.2 RS
Each part of resistance ‘R’ is equal to 0.2 times of original resistance. - Effective Resistance of 5 Resistors
`1/"R"_"P" = 1/"R" + 1/"R" + 1/"R" + 1/"R" + 1/"R" = 5/"R"`
`"R"_"P" = "R"/5` = 0.2 R - Effective resistance of series combination RS = 5R
Effective resistance of parallel combination
`"R"_"P" = "R"/5`
The ratio of series connection to the parallel connection
`"R"_"S"/"R"_"P" = (5"R")/("R"//"S")`
(2) (9 - R2 - + R2) = (9 - R2)R2
`"R"_"S"/"R"_"P" = 5 "R" xx 5/"R" = 25`
RS : RP = 25 : 1
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