Question

If the effective resistance of three resistors 3 ohms,5 ohms and Rohms connected in series
is 14 ohms, the value of 'R' is :

a) 6 ohms
b) 2 ohms
c) 4 ohms
d) 1 ohms​

Answer 1

Question :

If the effective resistance of three resistors 3ohms, 5ohms, and R ohms connected in series is 14ohms, the value of R is :

To find :

The value of R=?

Formula :

➡ When three resistors are connected in series then the effective resistance is :

$\\ \large\red\bigstar\boxed{\sf{R_{effective \: resistance } = R_1+R_2+R_3}}$

➡ when three resistors are connected in parallel then the effective resistance is:

$\\ \large\red\bigstar\boxed{\sf{R_{effective \: resistance } = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dfrac{1}{R_3} } }$

Solution :

$\red{\bf{Given}} \begin{cases} \sf{ R_1=3ohms} \\ \sf{R_2= 5ohms} \\ \sf{R_3=Rohms} \\ \sf{Effective \: resistance =14 ohms} \end{cases}$

$\\ \implies\large\sf{R_{effective \: resistance }= R_1 +R_2 +R_3 }$

➡ Substitute the given values :

$\\ \implies\large\sf{ R_{effective \: resistance }= 3+5+R_3}$

$\\ \implies\large\sf{ 14=8+R_3}$

$\\ \implies\large\sf{14-8-R_3 =0}$

$\\ \implies\large\sf{ R_3=14-8}$

$\\ \implies\large\sf{R_3=6ohms}$

$\\ \therefore\large\boxed{\underline{\sf{R_3=6ohms}}}$

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➡ Option (1) 6 ohms is correct answer ⛄

Answer 2

Answer:

The value of the 'R' of the third resistor = $6\Omega$.

Therefore, option a) $6ohms$ is correct.

Step-by-step explanation:

Given data,

The given resistance of the resistor 1, R₁ = $3\Omega$

The given resistance of the resistor 2, R₂ = $5\Omega$

The given resistance of the resistor 3, R₃ = $R\Omega$

The effective resistance of the given three resistors connected in series = $14\Omega$

The value of the resistance of the resistor 3, R₃ = $R\Omega$ =?

As we know, if the resistors are connected in series then their effective resistance will be:

• $R_{effective} = R_{1} + R_{2} + R_{3}$

After putting the values of the given resistances in the above-mentioned formula, we get:

• $14 = 3+5+R$
• R = $14-8$
• R = $6\Omega$

Hence, the value of the 'R' of the third resistor = $6\Omega$.

#SPJ3