A potential $V_0$ is applied across a uniform wire of resistance $R$. The power dissipation is $P_1$. The wire is then cut into two equal halves and a potential of $V _0$ is applied across the length of each half. The total power dissipation across two wires is $P_2$. The ratio $P_2: P_1$ is $\sqrt{x}: 1$. The value of $x$ is $.............$.
JEE MAIN 2023, Medium
Download our app for free and get started
$P=V I=I^2 R=\frac{V^2}{R}$
Now $R=\frac{\rho l}{A}$
If wire is cut in two equal half
$R^{\prime}=\frac{R}{2}$
Initial $P_1=\frac{V_0^2}{R}$
After $P_2=\frac{V_0^2}{R^{\prime}} \times 2 \Rightarrow \frac{V_0^2}{R} \times 4$
$\frac{P_2}{P_1}=4=\frac{\sqrt{x}}{1}$
$x=16$
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
- 1View SolutionThe equivalent resistance of the infinite network given below is :
- 2A battery of $e.m.f.$ $3\, volt$ and internal resistance $1.0\, ohm$ is connected in series with copper voltameter. The current flowing in the circuit is $1.5\, amperes$. The resistance of voltameter will be ........... $ohm$View Solution
- 3The Wheatstone bridge shown in Fig. here, gets balanced when the carbon resistor used as $R_1$ has the colour code (Orange, Red, Brown). The resistors $R_2$ and $R_4$ are $80\, \Omega $ and $40\,\Omega $, respectively. Assuming that the colour code for the carbon resistors gives their accurate values, the colour code for the carbon resistor, used as $R_3$ would beView Solution
- 4A horizontal conductor is oriented north south and carries some current. $A$ positively charged particle located vertically above it and having a velocity directed north ward experiences an upward force.What is the direction of the force if this charged particle were located to the east of the conductor and had a velocity directed towards the conductorView Solution
- 5What amount of heat will be generated in a coil of resistance $R$ due to a charge $q$ passing through it if the current in the coil decreases to zero uniformly during a time interval $\Delta t$View Solution
- 6The electromotive force of a primary cell is $2\, volts$. When it is short-circuited it gives a current of $4$ amperes. Its internal resistance in $ohms$ isView Solution
- 7In the circuit, given in the figure currents in different branches and value of one resistor are shown. Then potential at point $B$ with respect to the point $A$ is$.......V$View Solution
- 8The resistance of a wire is $5 \Omega$. It's new resistance in ohm if stretched to $5$ times of it's original length will be :View Solution
- 9In the circuit shown, $R_1$ is increased. What happens to the reading of the voltmeter (ideal)?View Solution
- 10Ten $60 \,W , 220 \,V$ bulbs are connected in series to $220 \,V$ supply. Power consumed in the circuit is ......... $W$View Solution