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[100]
Equivalent resistance $R_{eq}$ of two resistors with equal resistance $R$ are connected then __

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In parallel combination,

R_{p} = \frac{R}{2}

In series combination,

R_{s} = 2 R

R_{s} : R_{p} = 4 : 1

All of the above

answer is C.

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Detailed Solution

Equivalent resistance

R_{eq}

of two resistors with equal resistance

R

are connected then

R_{s} : R_{p} = 4 : 1

Let if two resistors are connected in series
The Equivalent resistance

{\Rightarrow R}_{s} = R_{1} + R_{2}

{\Rightarrow R}_{s} = R + R

[since it is given that two resistors with equal resistance

R

]

{\Rightarrow R}_{s} = 2 R

If two resistors are connected in parallel
The Equivalent resistance,

\frac{1}{R_{p}} = \frac{1}{R_{1}} + \frac{1}{R_{2}}

\Rightarrow \frac{1}{R_{p}} = \frac{1}{R_{}} + \frac{1}{R_{}}

\Rightarrow \frac{1}{R_{p}} = \frac{R + R}{R \times R}

\Rightarrow R_{p} = \frac{R}{2}

The ratio of equivalent resistance in series and parallel combination,

\frac{R_{s}}{R_{p}} = \frac{2 R}{\frac{R}{2}}

\Rightarrow \frac{R_{s}}{R_{p}} = \frac{4}{1}

Therefore

R_{s} : R_{p} = 4 : 1

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