Question

10 resistors of 2 ohms each are connected parallel.calculate the effective resistance

Answer 1

Answer:

1/R = 1/2+ 1/2 +1/2 +1/2 +1/2+ 1/2 +1/2 +1/2+ 1/2 +1/2= 10/2 = 5

1/R = 5

R = 1/5 ohm

Answer 2

Answer:

The effective resistance is 0.2Ω.

Explanation:

When the resistors are connected in parallel the voltage across the resistors is the same and the currents are different i.e. I₁, I₂,...Iₙ.

Where current is given as,

$I=\frac{V}{R}$                  (1)

Then the total current is given as,

$I=I_1+I_2+I_3+..........+I_n$         (2)

We can write equation (2) as,

$\frac{V}{R_e_q_v}=\frac{V}{R_1}+\frac{V}{R_2}+\frac{V}{R_3}+.....+\frac{V}{R_n}$

$\frac{1}{R_e_q_v}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+.....+\frac{1}{R_n}$

If n number of the resistors are of equal values then we can write equation (3) as,

$\frac{1}{R_e_q_v}=\frac{n}{R}$

$R_e_q_v=\frac{R}{n}$           (4)

From question,

R=2Ω

n=10

By substituting the value of n and R in equation (4) we get;

$R_e_q_v=\frac{2}{10}=0.2\Omega$

Hence, the effective resistance of 10 resistors of 2 ohms each is 0.2Ω.