A $1\,m$ long wire is broken into two unequal parts $X$ and $Y$ The $X$ part of the wire is streched into another wire $W$. Length of $W$ is twice the length of $X$ and the resistance of $W$ is twice that of $Y$. Find the ratio of length of $X$ and $Y$.
JEE MAIN 2022, Medium
Download our app for free and get started
$\frac{ R _{ X }}{ R _{ Y }}=\frac{\ell_{ X }}{\ell_{ Y }}$
When wire is stretched to double of its length, then resistance becomes 4 times
$R _{ W }=4 R _{ X }=2 R _{ Y }$
$\frac{ R _{ X }}{ R _{ Y }}=\frac{1}{2}$
So. $\frac{\ell_{ X }}{\ell_{ y }}=\frac{1}{2}$
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
- 1The value of current $i_{1}$ flowing from $A$ to $C$ in the circuit diagram is$.......A$View Solution
- 2What 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
- 3The charge accumulated on the capacitor connected in the following circuit is________ $\mu \mathrm{C}$ (Given $\mathrm{C}=150\ \mu \mathrm{F}$ )View Solution
- 4Potential difference across $A B$ i.e., $V_A-V_B$ is ......... $V$View Solution
- 5In the circuit shown, the point ‘$B$’ is earthed. The potential at the point ‘$A$’ is ............. $V$View Solution
- 6Four ammeters with identical internal resistance $r$ and a resistor $R$ are connected to a current source as given. if reading of $A_1$ and $A_2$ is $3\ A$ and $5\ A$ respectively then the reading $A_4$ is ............. $A$View Solution
- 7The figure shows a network of resistors and $a$ battery. If $1\,A$ current flowsthrough the branch $CF$, then answer the following questions The current throughView Solution
- 8Two batteries of different $e.m.f.'s$ and internal resistance connected in series with each other and with an external load resistor. The current is $3.0 \,A$. When the polarity of one battery is reversed, the current becomes $1.0 \,A$. The ratio of the $e.m.f.'s$ of the two batteries is ............View Solution
- 9The resistances of the platinum wire of a platinum resistance thermometer at the ice point and steam point are $8 \Omega$ and $10 \Omega$ respectively. After inserting in a hot bath of temperature $400^{\circ} \mathrm{C}$, the resistance of platinum wire is:View Solution
- 10A resistance $R = 12\, \Omega$ is connected across a source of emf as shown in the figure . Its $emf$ changes with time as shown in the graph . What is the heat developed in the resistance in the first four seconds ? ............. $J$View Solution
