Visit the website manishverma.site for latest posts, courses, admission & more.

$R_1 = (4\pm 0.8) \Omega$ $R_2 = (4\pm 0.4) \Omega$$R_{eq} =?$

Two resistors $R_1 = (4\pm 0.8) \Omega$ and $R_2 = (4\pm 0.4) \Omega$ are connected in parallel. The equivalent resistance of their parallel combination will be:

(A) $(4 \pm 0.4 ) \Omega$
(B) $(2 \pm 0.3 ) \Omega$
(C) $(4 \pm 0.3 ) \Omega$
(D) $(2 \pm 0.4 ) \Omega$

Solution

We have, $R=\frac {R_1 R_2}{R_1 + R_2 } = \frac {4 \times 4}{4+4} = 2 \Omega$

Further, $\frac {1}{R} = \frac {1}{R_1} + \frac {1}{R_2}$

$\therefore \frac {|\Delta R |}{R^2 }=\frac {|\Delta R_1 |}{R_1 ^2 } + \frac {|\Delta R_2 | }{R_2 ^2 }$

$\therefore \frac {|\Delta R |}{2^2 }=\frac {0.8}{4^2 } + \frac {0.4}{4^2 } = \frac {1.2}{16}$

$\therefore |\Delta R| = 0.3 \Omega$

$R_{eq} = R \pm |\Delta R | = 2 \pm 0.3 \Omega$

Sum of the coefficients in the expansion of $(x+y)^n$ ....
If the sum of the coefficients in the expansion of $(x+y)^n$ is 4096, then the greatest coefficient in the expansion is _ _ _ _ . Solution $C_0 + C_1 + C_2 + C_3 + ......................... + C_n =4096$ $\therefore 2^n = 4096 =2^{12}$ $\Rightarrow n = 12$ Greatest coefficient = ${}^{12}{C_6} = 924$