A wire of radius $r$ has resistance $R$. If it is stretched to a radius of $\frac{{3r}}{4}$, its resistance becomes
Medium
Download our app for free and get started
$\frac{{{R_1}}}{{{R_2}}} = {\left( {\frac{{{r_2}}}{{{r_1}}}} \right)^4}$ $ \Rightarrow $ $\frac{R}{{{R_2}}} = {\left( {\frac{{3r/4}}{r}} \right)^4} = \frac{{81}}{{256}} = {R_2} = \frac{{256}}{{81}}R$
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 figure shows a network of four resistances and three batteries Choose the correct alternative
- 2A potentiometer wire $AB$ having length $L$ and resistance $12\, r$ is joined to a cell $D$ of $emf$ $\varepsilon $ and internal resistance $r$. A cell $C$ having $emf$ $\varepsilon /2$ and internal resistance $3r$ is connected. The length $AJ$ at which the galvanometer as shown in figure shows no deflection isView Solution
- 3If resistance of voltmeter is $10000 \,\Omega$ and resistance of ammeter is $2 \,\Omega$ then find $R$ when voltmeter reads $12\,V$ and ammeter reads $0.1\, A$ ............... $\Omega$View Solution
- 4View SolutionIn a metallic conductor, under the effect of applied electric field, the free electrons of the conductor
- 5The current in a simple series circuit is $5.0\, amp$. When an additional resistance of $2.0\, ohms$ is inserted, the current drops to $4.0\, amp$. The original resistance of the circuit in $ohms$ wasView Solution
- 6The number of dry cells, each of $e.m.f.$ $1.5\,volt$ and internal resistance $0.5\, ohm$ that must be joined in series with a resistance of $20\, ohm$ so as to send a current of $0.6\,A$ through the circuit isView Solution
- 7Resistors of $1$, $2$, $ohm$ are connected in the form of a triangle. If a $1.5\, volt$ cell of negligible internal resistance is connected across $3\, ohm$ resistor, the current flowing through this resistance will be ................ $amp$View Solution
- 8Every atom makes one free electron in copper. If $1.1$ $ampere$ current is flowing in the wire of copper having $1\, mm$ diameter, then the drift velocity (approx.) will be (Density of copper $ = 9 \times {10^3}\,kg\,{m^{ - 3}}$ and atomic weight = $63$)View Solution
- 9In the balanced condition, the values of the resistances of the four arms of a Wheatstone bridge are shown in the figure below. The resistance $R_3$ has temperature coefficient $0.0004{ }^{\circ} C ^{-1}$. If the temperature of $R_3$ is increased by $100{ }^{\circ} C$, the voltage developed between $S$ and $T$ will be. . . . . . . volt.View Solution
- 10A wire of resistance $10$ $\Omega$ is bent to form a circle. $P$ and $Q$ are points on the circumference of the circle dividing it into a quadrant and are connected to a Battery of $3\, V$ and internal resistance $1$ $\Omega$ as shown in the figure. The currents in the two parts of the circle areView Solution
