A fuse wire of radius 0.2 ,mm blows off with | vedclass

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

Question

(C) The heat produced in a fuse wire is given by $H = I^2 R t$. The fuse wire blows off when the heat generated reaches a critical value, which is pro

Vedclass · Accepted Answer

$5 \sqrt{\frac{27}{8}} \,A$

Vedclass · Answer

(C) The heat produced in a fuse wire is given by $H = I^2 R t$. The fuse wire blows off when the heat generated reaches a critical value, which is proportional to the surface area of the wire for heat dissipation. Thus, $I^2 R \propto r^2$. Since resistance $R = \rho \frac{l}{A} = \rho \frac{l}{\pi r^2}$, we have $I^2 \left(\frac{1}{r^2}\right) \propto r^2$, which implies $I^2 \propto r^3$ or $I \propto r^{3/2}$.Given $r_1 = 0.2 \,mm$, $I_1 = 5 \,A$, and $r_2 = 0.3 \,mm$.Using the ratio $\frac{I_2}{I_1} = \left(\frac{r_2}{r_1}\right)^{3/2}$:$\frac{I_2}{5} = \left(\frac{0.3}{0.2}\right)^{3/2} = \left(\frac{3}{2}\right)^{3/2} = \sqrt{\frac{27}{8}}$.Therefore, $I_2 = 5 \sqrt{\frac{27}{8}} \,A$.

$A$ fuse wire of radius $0.2 \,mm$ blows off with a current of $5 \,A$. The fuse wire of the same material but of radius $0.3 \,mm$ will blow off with a current of:

Similar Questions

$A$ cell of $emf$ $E$ and internal resistance $r$ is connected in series with an external resistance $nr$. Then,the ratio of the terminal potential difference to $emf$ is

In the circuit shown in the figure,no current flows through the ideal ammeter. If the internal resistance of the cell is negligible,the value of unknown resistance $R$ is .............. $\Omega$.

$A$ battery of $e.m.f.$ $10 \, V$ and internal resistance $3 \, \Omega$ is connected to a resistor $R$ as shown in the figure. If the current in the circuit is $0.5 \, A$,then the resistance of the resistor $R$ will be ............. $\Omega$.

In the given circuit,the voltmeter records $5 \, V$. The resistance of the voltmeter in $ohms$ is

Two bulbs are in parallel and they together consume $48\, W$ from a battery of $6\, V$. The resistance of each bulb is ............ $\Omega$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module