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### College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

# (a) What is the resistance of ten ${\mathbf{275}}{\mathbf{-}}{\mathbf{\Omega }}$resistors connected in series? (b) In parallel?

(a)The resistance of ten $275\Omega$resistors connected in series is $2750\Omega$.

(b)The resistance of ten $275\Omega$ resistors connected in parallel is $27.50\Omega$.

See the step by step solution

## Step 1: Definition of resistance in series and parallel

An unwillingness to accept anything, such as a change or a new thought, is known as resistance.

Resistance in series: When resistors are daisy-chained together in a single line and a common current flows through them, they are said to be connected in series.

Resistance in parallel: In a parallel circuit, the total resistance is always less than any of the branch resistances. The total resistance in the circuit decreases when more parallel resistances are added to the lines.

## Step 2: Finding resistance of resistors connected in series

(a)

The equivalent resistance of the n resistors with each of resistance and connected in series can be expressed as,

${\mathrm{R}}_{\mathrm{s}}=\mathrm{nR}$

Therefore, substituting the given data, we will get,

${R}_{s}=10×275\phantom{\rule{0ex}{0ex}}=2750\Omega$

Thus, the resistance of ten $275\Omega$ resistors connected in series is $2750\Omega$.

## Step 3: Finding resistance of resistors connected in parallel

(b)

The equivalent resistance of the n resistors with each of resistance and connected in parallel can be expressed as,

${\mathrm{R}}_{\mathrm{P}}=\frac{\mathrm{R}}{\mathrm{n}}$

Therefore, substituting the given data, we will get,

${\mathrm{R}}_{\mathrm{P}}=\frac{275\mathrm{\Omega }}{10}\phantom{\rule{0ex}{0ex}}=27.50\mathrm{\Omega }$

Hence, the resistance of ten$275\Omega$resistors connected in parallel is$27.50\Omega$.
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