Question

two 50 ohm resistors are connected in series.When a resistor,R is connected in parallel with the combination ,the equivalent resistance of the circuit is 60 ohms.Calculate the value of R.

Answer 1

Answer:

Two 50 ohm resistors are connected in series. When a resistor R is connected in parallel with the combination, the equivalent resistance of the circuit is 60 ohms, then the value of R is 150Ω

Explanation:

• A resistor is  used to resist the current flow through  a circuit

• If two resistors with resistances $R_{1} ,R_{2}$ are connected in parallel in a circuit the effective resistance that appeared in the circuit is given by the formula

        $1/R_{eff} =1/R_{1} +1/R_{2}$

        ⇒$R_{eff} =\frac{R_{1} R_{2} }{R_{1} +R_{2} }$

• If they are connected in series the effective resistance is $R_{eff} =R_{1} +R_{2}$

from the question, we have given that

the value of a resistance connected in series  $R=50$Ω

effective resistance $R_{s}=50+50=100$Ω

the effective resistance of the circuit $R_{eff} =60$ Ω

now the new resistances R and $R_{s}$ are in parallel

substitute the given values to get the resistance  newly introduced

⇒$60=\frac{R_{s}*R }{R_{s} +R }$

⇒$60*R_{s} +60*R =R*R_{s}$

⇒

$6000=40R\\ R=6000/40=150$