Math, asked by adityapatil9059, 2 months ago

Rohan has three resistors, each of resistance 4 omp draw and show the working of how he would join these three resistors to get an equivalent resistance of 6 omp​

Answers

Answered by itzreha08
2

Answer

To obtain a combined resistance of 9 ohms, three resistors each of resistance 6 ohm should be connected in a parallel circuit and one in series.

In a parallel circuit, the equivalent resistance of all the resistors connected is equal to the reciprocal value of the sum of the individual resistances.

In a series circuit, the equivalent resistance of all the resistors connected is equal to the sum of the resistance values of each of the individual resistor.

So in a parallel circuit, total resistance =

 \frac{1}{Rt} =  \frac{1}{R1} +  \frac{1}{R2} +  \frac{1}{R3}

or

R t =

 \frac{1}{R1}  +  \frac{1}{R2}  +  \frac{1}{R3}

In a series circuit, total resistance = R1 +R2 + R3

(i) To get 9 ohms, two resistors should be connected in parallel and one in series.

So,

Rt in parallel will be

Rt =  \frac{1}{ \frac{1}{R1} +  \frac{1}{R2}  }   =  \frac{1}{ \frac{1}{6}  +  \frac{1}{6} }

= 3 ohms

One resistor is connected in series with the 3 ohms, so

Rt in series will be Rt = R1 +R2 = 6+3 = 9 ohms

(ii) To obtain a combined resistance of 4 ohms, two resistors (of 6 ohms each) are connected in series and one in parallel to the series.

So,

Rt in series = R1 +R2 = 6+6 = 12 ohms

Rt \: in \: parallel \:  =  \frac{1}{Rt}  =  \frac{1}{R1} +  \frac{1}{R2} =  \frac{1}{6} +  \frac{1}{12}  = 4 \:  \: Ohms

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