Question

the resistor having resistances of of 12 ohm 18 ohm and 10 ohm find its effective resistance​

Answer 1

Correct Question:-

The resistor having resistances of 12 $\Omega$, 8 $\Omega$ and $\omega$ connected in parallel. Find it's effective resistance.

Note:-

Refer to the attachment for the diagram.

Solution:-

We know,

Equivalent Resistance in a parallel connection is calculated using formula:-

$\sf{\dfrac{1}{R_p} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + ........ \dfrac{1}{R_n}}$

Here in this diagram,

$\sf{R_1 = 12\Omega}$

$\sf{R_2 = 18\Omega}$

$\sf{R_3 = 10\Omega}$

Now,

Equivalent (or effective) Resistance across the resistor,

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

= $\sf{\dfrac{1}{R_p} = \dfrac{1}{12} + \dfrac{1}{18} + \dfrac{1}{10}}$

= $\sf{\dfrac{1}{R_p} = \dfrac{15+10 + 18}{180}}$

= $\sf{\dfrac{1}{R_p} = \dfrac{43}{180}}$

= $\sf{R_p = \dfrac{180}{43}}$

= $\sf{R_p = 4.2\Omega}$

Therefore the effective resistance across the resistor is 4.2 Ω

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Extra Information!!!

Equivalent Resistance in series is calculated by using the formula:-

$\sf{R_s = R_1 + R_2 + R_3 ......... R_n }$

✭In a series connection, the voltage remains constant and the electricity flowing through it gets distributed.

✭ In a parallel connection, the electricity remains constant and the voltage through it resistor gets distributed.

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