In the circuit shown, the resistance r is a variable resistance. If for r = f R, the heat generation in r is maximum then the value of f is :

Question

In the circuit shown, the resistance r is a variable resistance. If for r = f R, the heat generation in r is maximum then the value of f is : (A) (1/4) (B) (1/2) (C) (3/4) (D) 1

Tardigrade Admin · Accepted Answer

Heat generation in r will be, H = I r 2 r, H=(( V / R +( Rr ) R + r ) × ( r / R + r ))2 r =(( V / R ( R +2 r )))2 r Putting ( dH / dr )=0 gives, r =( R /2). Hence, f =(1/2).

Q. In the circuit shown, the resistance $r$ is a variable resistance. If for $r = f R$ , the heat generation in $r$ is maximum then the value of $f$ is :

$\frac{1}{4}$

$\frac{1}{2}$

$\frac{3}{4}$

$1$

Heat generation in $r$ will be, $H = I_{r}^{2} r$ ,
$H = (\frac{V}{R + \frac{R r}{R + r}} \times \frac{r}{R + r})^{2} r = (\frac{V}{R ( R + 2 r )})^{2} r$
Putting $\frac{d H}{d r} = 0$ gives, $r = \frac{R}{2}$ . Hence, $f = \frac{1}{2}$ .

Q. In the circuit shown, the resistance r is a variable resistance. If for r=fR, the heat generation in r is maximum then the value of f is :

41​

21​

43​

1

Heat generation in r will be, H=Ir2​r, H=(R+R+rRr​V​×R+rr​)2r=(R(R+2r)V​)2r Putting drdH​=0 gives, r=2R​. Hence, f=21​.

Q. In the circuit shown, the resistance $r$ is a variable resistance. If for $r = f R$ , the heat generation in $r$ is maximum then the value of $f$ is :

$\frac{1}{4}$

$\frac{1}{2}$

$\frac{3}{4}$

$1$

Heat generation in $r$ will be, $H = I_{r}^{2} r$ ,
$H = (\frac{V}{R + \frac{R r}{R + r}} \times \frac{r}{R + r})^{2} r = (\frac{V}{R ( R + 2 r )})^{2} r$
Putting $\frac{d H}{d r} = 0$ gives, $r = \frac{R}{2}$ . Hence, $f = \frac{1}{2}$ .