Question

If Rs and Rp equivalent resistance of two resistors of 4ohm in 6ohm when connected in series and parallel respectively ,find the ratio of Rs and Rp

Answer 1

Given that, Rs and Rp equivalent resistance of two resistors of 4 ohm in 6 ohm when connected in series and parallel respectively.

We have to find the ratio of Rs and Rp.

Rs = R1 + R2 = 4

→ R1 + R2 = 4

Similarly,

1/Rp = 1/R1 + 1/R2 = 6

→ 1/R1 + 1/R2 = 6

→ (R2 + R1)/(R1R2) = 6

→ 4/(R1R2) = 6

→ R1R2 = 4/6

→ R1R2 = 2/3

Now,

Rs/Rp = 4/(2/3)

Rs/Rp = 12/2

Rs/Rp = 6/1

Therefore, the ratio of Rs and Rp is 6:1.

Answer 2

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QUESTION :

If Rs and Rp equivalent resistance of two resistors of 4ohm in 6ohm when connected in series and parallel respectively ,find the ratio of Rs and Rp.

SOLUTION :

From the above Question, we can gather the following information...

If Rs and Rp equivalent resistance of two resistors of 4ohm in 6ohm when connected in series and parallel respectively.

We know that :

Sum of resistances in series :

R_{ Equivalent } = R_{1} + R_{2} +.....

Sum of resistances in parallel ;

1 / R_ { Equivalent } = 1 / { R 1 } + 1 / { R 2 } + ....

Here, There are only two Resistances , R_{1} and R_{2}

Now, from the question ...

R_{1} + R_{2} = 4 Ohm = r_{S}

1 / R_{ 1 } + 1 / R _ { 2 } = 6 Ohm = R _ { p }

In the second case, we can now take LCM

=> [ R_{1} + R_{2} ] / [ R_{1} × R _ { 2 } ] = 6

=> Substuting the first value here :

=> 4 / { R_{ 1} × R _ { 2 } } = 6

=> R_{1} × R_{2} = 2 / 3

Now, we need to find the value of :

=> [ R _ { S } / R _ { P } ]

=> 4 / { 2 / 3 }

=> { 12 / 2 }

=> 6

So, The ratio Of R _ { S } and R _ { P } is equal to 6 : 1

ANSWER :

The ratio Of R _ { S } and R _ { P } is equal to 6 : 1