Question

Q.13. You are given n identical wires, each of resistance R.
When these are connected in parallel, the equivalent resistance is X. When these will
be connected in series, then the equivalent resistance will be
(a) X/n²
(b) n
(c) x/n
(d) nx​

Answer 1

Question:

You are given n identical wires each of resistance R. When these are connected in parallel, the equivalent resistance is X. When these will be connected in series, the equivalent resistance will be?

Options:

a) X/n²

b) n

c) X/n

d) nX

e) Xn²

Answer:

$\bigstar{\bold{Option\:E=Xn^{2} }}$

Explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• Resistors are identical
• Total Resistance = X when resistors are connected in parallel

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• Equivalent resistance when resistors are connected in series

$\Large{\underline{\underline{\bf{Solution:}}}}$

→ Equation when n resistors are connected in parallel is given by

  Equivalent resistance = R/n

→ Equation when n resistors are conected in series is given by

  Equivalent resistance = R × n----equation 1

→ But given that R/n = X

→ Therefore R = X n

→ Substitute the value of R in equation 1

 Equivalent resistance = X × n × n

$\boxed{\bold{Equivalent\:resistance=Xn^{2} }}$

Hence option E is correct.

$\Large{\underline{\underline{\bf{Notes:}}}}$

→ When resistors are connected in series, equivalent resistance is given by

   $R=R_1+R_2+R_3+.......+R_n$

→ When resistors are connected in parallel, equivalent resistance is given by

   $\dfrac{1}{R} =\dfrac{1}{R_1} +\dfrac{1}{R_2} +\dfrac{1}{R_3}+......+\dfrac{1}{R_n}$