The equivalent resistance of n resistors each of same resistance when connected in series is R . If the same resistances are connected in parallel, the equivalent resistance will be

Question

The equivalent resistance of n resistors each of same resistance when connected in series is R . If the same resistances are connected in parallel, the equivalent resistance will be (A) R / n2 (B) R / n (C) n2 R (D) n R

Tardigrade Admin · Accepted Answer

Effective resistance of n resistance each of the resistance r in series Rs=r × n=R (as per question); so r=R / n . When these resistances are connected in parallel, the effective resistance Rp=(r/n)=(R / n/n)=(R/n2)

Q. The equivalent resistance of $n$ resistors each of same resistance when connected in series is $R .$ If the same resistances are connected in parallel, the equivalent resistance will be

$R / n^{2}$

$R / n$

$n^{2} R$

n R

Effective resistance of $n$ resistance each of the resistance $r$ in series $R_{s} = r \times n = R$ (as per question); so $r = R / n .$ When these resistances are connected in parallel, the effective resistance
$R_{p} = \frac{r}{n} = \frac{R / n}{n} = \frac{R}{n ^{2}}$

Q. The equivalent resistance of n resistors each of same resistance when connected in series is R. If the same resistances are connected in parallel, the equivalent resistance will be

R/n2

R/n

n2R

n R

Effective resistance of n resistance each of the resistance r in series Rs​=r×n=R (as per question); so r=R/n. When these resistances are connected in parallel, the effective resistance Rp​=nr​=nR/n​=n2R​

Q. The equivalent resistance of $n$ resistors each of same resistance when connected in series is $R .$ If the same resistances are connected in parallel, the equivalent resistance will be

$R / n^{2}$

$R / n$

$n^{2} R$

Effective resistance of $n$ resistance each of the resistance $r$ in series $R_{s} = r \times n = R$ (as per question); so $r = R / n .$ When these resistances are connected in parallel, the effective resistance
$R_{p} = \frac{r}{n} = \frac{R / n}{n} = \frac{R}{n ^{2}}$