Question

6 Three resistances of 4, 6, 12
are connected in parallel across DC supply of 24v. Find effective resistence​

Answer 1

Explanation:

effective resistance

1/R=1/4+1/6+1/12

R=2ohm

Answer 2

${\underline {\underline {\huge {\bf { Required \: Answer: } }}}}$

Given:

• Three resistances of 4Ω, 6Ω and 12Ω are connected in parallel series.

To Calculate:

• Total effective resistance

Calculation:

We know that,

• ${\boxed {\large {\bf {\purple { \dfrac{1}{R_p} = \dfrac{1}{R_1} +\dfrac{1}{R_2} +\dfrac{1}{R_3} ..........}}}}}$

Where,

• $\bf { R_1 \longrightarrow 4Ω}$
• $\bf { R_2 \longrightarrow 6Ω}$
• $\bf { R_3 \longrightarrow 12Ω}$

Substitute the values:

$\bf { ⇢ \dfrac{1}{R_p} = \dfrac{1}{R_1} +\dfrac{1}{R_2} +\dfrac{1}{R_3}}$

⠀⠀⠀

⠀⠀⠀

$\bf { ⇢ \dfrac{1}{R_p} = \dfrac{1}{4} +\dfrac{1}{6} +\dfrac{1}{12}}$

⠀⠀⠀

⠀⠀⠀

$\bf { ⇢ \dfrac{1}{R_p} = \dfrac{3+2+1}{12} }$

⠀⠀⠀

⠀⠀⠀

$\bf { ⇢ \dfrac{1}{R_p} = \dfrac{6}{12} }$

⠀⠀⠀

⠀⠀⠀

$\bf { ⇢ R_p = \dfrac{12}{6} }$

⠀⠀⠀

⠀⠀

${\underline {\boxed {\large {\bf { R_p = 2Ω} }}}}$

Therefore, total effective resistance is of 2Ω.

_________________________________

More Information:

• The property of a conductor due to which it opposes the flow of current through it is called resistance.
• The resistance of a conductor depends on the length thickness temperature and nature of the material of the conductor.
• The SI unit of resistance is ohm (Ω).

• The resistance can be into combination:

✤ Series Combination:

The sum of individual resistances is equal to the total resistance in the series combination.

Formula: ${\boxed {\large {\bf {\purple { R_s = R_1 + R_2 + R_3..........}}}}}$

✤ Parallel Combination:

The sum of reciprocals of all the individual resistances is equal to the reciprocal of the total resistance in the parallel combination.

Formula: ${\boxed {\large {\bf {\purple { \dfrac{1}{R_p} = \dfrac{1}{R_1} +\dfrac{1}{R_2} +\dfrac{1}{R_3} ..........}}}}}$

____________________________________