The same mass of copper is drawn into two wires $1\, mm$ and $2\, mm$ thick. Two wires are connected in series and current is passed through them. Heat produced in the wire is in the ratio
Medium
Download our app for free and get started
(d) $H = {i^2}RT = {i^2}\left( {\frac{{\rho l}}{A}} \right)\,t = \frac{{{i^2}\rho Vt}}{{{A^2}}}$ $(V =$ volume, $= Al)$
$ \Rightarrow $ $H \propto \frac{1}{{{r^4}}}$ $ \Rightarrow $ $\frac{{{H_1}}}{{{H_2}}} = {\left( {\frac{{{r_2}}}{{{r_1}}}} \right)^4} = {\left( {\frac{2}{1}} \right)^4} = \frac{{16}}{1}$.
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1A potentiometer wire has length $10\, m$ and resistance $20\,\Omega $. A $2. 5\, V$ battery of negligible internal resistance is connected across the wire with an $80\,\Omega $ series resistance. The potential gradient on the wire will beView Solution
- 2Five equal resistances are connected in a network as shown in figure. The net resistance between the points $A$ and $B$ isView Solution
- 3In the circuit shown below $E_1\, =4.0\, V$, $R_1\, = 2\,\Omega$, $E_2\, = 6.0\, V$, $R_2\, = 4\,\Omega$ and $R_3\, = 2\,\Omega$. The current $I_1$ is ............... $\mathrm{A}$View Solution
- 4A $2\, W$ carbon resistor is color coded with green, black, red and brown respectively. The maximum current which can be passed through this resistor is .............. $mA$View Solution
- 5A battery of $e.m.f.$ $10\, V$ and internal resistance $0.5\, ohm$ is connected across a variable resistance $R$. The value of $R$ for which the power delivered in it is maximum is given by ......... $ohm$View Solution
- 6In the given figure of meter bridge experiment, the balancing length $AC$ corresponding to null deflection of the galvanometer is $40\,cm$. The balancing length, if the radius of the wire $AB$ is doubled, will be $....cm$View Solution
- 7The $H$ amount of thermal energy is developed by a resistor in $10\,s$ when a current of $4\,A$ is passed through it. If the current is increased to $16\,A$, the thermal energy developed by the resistor in $10\,s$ will be $........\,H$View Solution
- 8In the given figure, the $emf$ of the cell is $2.2\, {V}$ and if internal resistance is $0.6\, \Omega$. Calculate the power dissipated in the whole circuit: (in $W$)View Solution
- 9A current of $1\, mA$ is flowing through a copper wire. How many electrons will pass a given point in one secondView Solution
- 10In a potentiometer (see figure) a balance is obtained at a length of $400\ mm$ when using a known battery of emf $1.6\ V$. After removing this battery, another battery of unknown emf is used and balance is obtained at a length of $650\ mm.$ The emf of unknown battery is ............. $volt$View Solution
