Two resistances R 1 and R 2 give a combined resistance of 4-5 - when in series and 1 - when in parallel- The value of resistances areA- 3 - 6 -B- 3 - 9 -C- 1-5 - 0-5 -D- 1-5 - 3 -

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Combination of resistors

Two resistanc...

Question

Two resistances $R_{1}$ and $R_{2}$ give a combined resistance of 4.5 $Ω$ when in series and 1 $Ω$ when in parallel. The value of resistances are___________.

3 , 6

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3 , 9

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1.5 , 3

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1.5 , 0.5

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Solution

The correct option is C
1.5 , 3

For series combination, $R_{e q}$ = $R_{1}$ + $R_{2}$

4.5 = $R_{1}$ + $R_{2}$

For parallel combination, $R_{e q} = \frac{R_{1} R_{2}}{R_{1} + R_{2}}$

1 = $\frac{R_{1} R_{2}}{4.5}$

$R_{1}$ = $\frac{4.5}{R_{2}}$

Substituting and solving we get,

$R_{1}$ = 1.5 $Ω$ , $R_{2}$ = 3 $Ω$

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Two resistances R1 and R2 give a combined resistance of 4.5 Ω when in series and 1 Ω when in parallel. The value of resistances are___________.​

The correct option is C 1.5 , 3 For series combination, Req= R1 + R2 4.5 = R1 + R2 For parallel combination, Req=R1R2R1+R2 1 = R1R24.5 R1= 4.5R2 Substituting and solving we get, R1= 1.5 Ω, R2= 3 Ω

Two resistances $R_{1}$ and $R_{2}$ give a combined resistance of 4.5 $Ω$ when in series and 1 $Ω$ when in parallel. The value of resistances are___________.