Question

Find the sum of the resistance of 6ohm,9ohm,4ohm when connected in parallel​

Answer 1

Given :

Three resistances of 6Ω, 9Ω and 4Ω are connected in parallel.

To Find :

Equivalent resistance of the parallel connection.

Solution :

★ The reciprocal of the combined resistance of a number of resistance connected in parallel is equal to the sum of the reciprocal of all the individual resistances. i.e.,

$\dag\:\underline{\boxed{\bf{\orange{\dfrac{1}{R_1}+\dfrac{1}{R_2}+...+\dfrac{1}{R_n}=\dfrac{1}{R}}}}}$

By substituting the given values;

➝ 1/R = 1/R₁ + 1/R₂ + 1/R₃

➝ 1/R = 1/6 + 1/9 + 1/4

➝ 1/R = (6 + 4 + 9) / 36

➝ R = 36/19

➝ R = 1.89 Ω

Knowledge BoosteR :

• In series combination, current through each resistor is same but potential differences across the resistors may be different.
• In parallel combination, potential difference on each resistor is same but the current through resistors may be different.

Answer 2

Given :

Three resistances of 6Ω, 9Ω and 4Ω are connected in parallel.

To Find :

Equivalent resistance of the parallel connection.

Solution :

★ The reciprocal of the combined resistance of a number of resistance connected in parallel is equal to the sum of the reciprocal of all the individual resistances. i.e.,

1 R1+ 1 R2+...+ 1R n

= 1/R

By substituting the given values;

➝ 1/R = 1/R₁ + 1/R₂ + 1/R₃

➝ 1/R = 1/6 + 1/9 + 1/4

➝ 1/R = (6 + 4 + 9) / 36

➝ R = 36/19

➝ R = 1.89 Ω

Knowledge BoosteR :

In series combination, current through each resistor is same but potential differences across the resistors may be different.

In parallel combination, potential difference on each resistor is same but the current through resistors may be different.