Question

When resistors 1 and 2 are connected in series, the equivalent resistance is 20.4 Ω. When they are connected in parallel, the equivalent resistance is 3.86 Ω. What are (a) the smaller resistance and (b) the larger resistance of these two resistors?

Answer 1

Answer:

(A) Smaller resistance will be equal to 5.175 ohm

(b) Larger resistance will be equal to 15.225 ohm  

Explanation:

Let the two resistances are $R_1$ and $R_2$

It is given that when they are connected in series their equivalent resistance is 20.4 ohm

So $R_!+R_2=20.4$------eqn 1

When they are connected in parallel their equivalent resistance is  3.86 ohm

So $\frac{R_!R_2}{R_1+R_2}=3.86$

From equation 1

$R_1R_2=3.86\times 20.4=78.744$

$R_1-R_2=\sqrt{(R_1+R_2)^2-4R_!R_2}=\sqrt{(20.4)^2-4\times 78.744}=10.05$ ......eqn 2

Adding eqn 1 and eqn 2

$2R_1=30.45$

$R_1=15.225ohm$ putting this value in eqn 1

$R_2=20.4-15.225=5.175ohm$

(a) Smaller resistance will be equal to 5.175 ohm

(b) Larger resistance will be equal to 15.225 ohm