Question

When two resistors connected in series and parallel their effective resistance are 15 Ω

and 56
/15
Ω respectively. Find the individual resistance of the resistors.
​

Answer 1

${\huge{\underline{\purple{\bf\tt{Question:} } }}}$

When two resistors connected in series and parallel their effective resistance are 15 Ω and 56/15Ω respectively. Find the individual resistance of the resistors.

${\huge{\underline{\orange{\bf\tt{Solution:} } }}}$

Let the two resistors be R and r

A/Q

When connected in series:

Equivalent resistance=R+r=15 ___(i)

When connected in parallel:

Equivalent resistance $\downarrow$

$\sf \frac{1}{R}+\frac{1}{r}=\frac{1}{R_e} \\\\\sf \frac{R+r}{Rr}= \frac{15}{56} \\\\\sf Rr=56----(ii) \\\\\sf From~(i) ~, R=15-r \\\\\sf Putting~R=15-r~ in~(ii),~we~get: \\\\\sf (15-r)r=56 \\\\\sf 15r-r^2-56=0 \\\\\sf r^2-15r+56=0 \\\\\sf r^2-8r-7r+56=0 \\\\\sf r(r-8)-7(r-8) \\\\\sf (r-7)(r-8) \\\\\sf r = 7~ or ~r=8 \\\\\sf If~ we ~put~ the~ value~ of~ r ~in~ (i), ~we~get~R=7 or 8$

We have R=7Ω and r=8 Ω

Or

We have R=8Ω and r=7Ω