Question

A) Three resistance 2ohm, R2, and 5ohm are connected in series,
their effective resistance is 10 ohm what is the value of R₂?
b) What will be the effective resistance if they are connected
in parallel?​

Answer 1

Answer:

a) 3 ohms

b) 30/31 ohms

Explanation:

(a) Effective resistance of n resistances connected in series formula is :

Req = R1 + R2 + R3 + .... + Rn

⇒ 10 = 2 + R2 + 5

⇒ 10 = 7 + R2

∴ R2 = 3 ohms.

(b) As R1 = 2 ohms

R2 = 3 ohms

R3 = 5 ohms

Effective resistance when n resistances connected in parallel formula is :

$\frac{1}{R_{eq} } = \frac{1}{R_1}} + \frac{1}{R_{2}} + ... + \frac{1}{R_{n}}$

⇒ $\frac{1}{R_{eq} }$ = $\frac{1}{2} + \frac{1}{3} + \frac{1}{5}$

⇒ $\frac{1}{R_{eq}}$ = $\frac{15 + 10 + 6}{30}$

⇒ $\frac{1}{R_{eq}}$ = $\frac{31}{30}$

∴ Effective Resistance = 30/31 ohms.

Thanks !