The resistance of a device component decrease | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given,the resistance $R$ of a device is related to the current $I$ by the relation: $R = \frac{0.2 I}{I-4}$.Power $P$ consumed by the device is gi

Vedclass · Accepted Answer

$21.6$

Vedclass · Answer

(D) Given,the resistance $R$ of a device is related to the current $I$ by the relation: $R = \frac{0.2 I}{I-4}$.Power $P$ consumed by the device is given by $P = I^2 R$.Substituting the expression for $R$: $P = I^2 \left( \frac{0.2 I}{I-4} ight) = \frac{0.2 I^3}{I-4}$.To find the minimum power,we differentiate $P$ with respect to $I$ and set it to zero: $\frac{dP}{dI} = 0$.$\frac{d}{dI} \left( \frac{0.2 I^3}{I-4} ight) = 0$.Using the quotient rule: $\frac{(I-4)(0.6 I^2) - (0.2 I^3)(1)}{(I-4)^2} = 0$.$0.6 I^3 - 2.4 I^2 - 0.2 I^3 = 0$.$0.4 I^3 - 2.4 I^2 = 0$.$0.4 I^2 (I - 6) = 0$.Since $I > 4$,we have $I = 6 \ A$.Substituting $I = 6 \ A$ into the power equation: $P_{\min} = \frac{0.2 	imes (6)^3}{6-4} = \frac{0.2 	imes 216}{2} = 0.2 	imes 108 = 21.6 \ W$.

The resistance of a device component decreases as the current through it increases and it is described by the relation,$R = \frac{0.2 I}{I-4}$,where $I$ is the current. Determine the minimum power delivered. (Assume $I > 4$) (in $W$)

Similar Questions

If the electric current in a lamp decreases by $5 \ \%$,then the power output decreases by . . . . . . . (in $\%$)

$A$ heater coil is cut into two equal parts and only one part is now used in the heater. The heat generated will now be

How much work is required to carry a $6 \mu C$ charge from the negative terminal to the positive terminal of a $9 V$ battery?

If two electric bulbs have $40\,W$ and $60\,W$ ratings at $220\,V$,then the ratio of their resistances will be

An electric kettle takes $4 \ A$ current at $220 \ V$. If the entire electric energy is converted into heat energy, then the time (in minutes) taken to increase the temperature of $1 \ kg$ of water from $34^{\circ} C$ to $100^{\circ} C$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module