A material '$B$' has twice the specific resistance of '$A$'. A circular wire made of '$B$' has twice the diameter ofa wire made of '$A$'. then for the two wires to have the same resistance, the ratio $\frac{{{l_B}}}{{{l_A}}}$ of their respective lengths must be
AIEEE 2006, Medium
Download our app for free and get started
$\rho_{B}=2 \rho_{A}$
$d_{B}=2 d_{A}$
$R_{B}=R_{A} \Rightarrow \frac{\rho_{B} \ell_{B}}{A_{B}}=\frac{\rho_{A} \ell_{A}}{A_{A}}$
$\therefore \frac{\ell_{B}}{\ell_{A}}=\frac{\rho_{A}}{\rho_{B}} \times \frac{d_{B}^{2}}{d_{A}^{2}}=\frac{\rho_{A}}{2 \rho_{A}} \times \frac{4 d_{A}^{2}}{d_{A}^{2}}=2$
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 electric current through a wire varies with time as $I=I_0+\beta t$. where $I_0=20 \mathrm{~A}$ and $\beta=3 \mathrm{~A} / \mathrm{s}$. The amount of electric charge crossed through a section of the wire in $20 \mathrm{~s}$ is :View Solution
- 2A cell of internal resistance $r$ is connected across an external resistance $n r$. Then the ratio of the terminal voltage to the emf of the cell isView Solution
- 3A galvanometer $(G)$ $\Omega$ of 2 risistance is connected in the givn circuit the raito of charge in $C_1$ and $C_2$ is:View Solution
- 4$A$ total charge $Q$ flows across a resistor $R$ during a time interval $= T$ in such a way that the current vs. time graph for $0 \rightarrow T$ is like the loop of a sin curve in the range $0 \rightarrow \pi$ . The total heat generated in the resistor isView Solution
- 5A light bulb of resistance $R=16 \,\Omega$ is attached in series with an infinite resistor network with identical resistances $r$ as shown below. A $10 \,V$ battery drives current in the circuit. ............. $\Omega$ the value of $r$ such that the bulb dissipates about $1 \,W$ of power.View Solution
- 6Two wires $A$ and $B$ of same material and mass have their lengths in the ratio $1 : 2$. On connecting them to the same source, the rate of heat dissipation in $B$ is found to be $5\,W$. The rate of heat dissipation in $A$ is............ $W$View Solution
- 7The current in the primary circuit of a potentiometer is $0.2\, A$. The specific resistance and cross section of the potentiometer wire are $4\times10^{-7}\,ohm$ $metre$ and $8\times10^{-7}\, m^2$ respectively. The potential gradient will be equal to .............. $V/m$View Solution
- 8Two long coaxial and conducting cylinders of radius $a$ and $b$ are separated by a material of conductivity $\sigma$ and a constant potential difference $V$ is maintained between them, by a battery. Then the current, per unit length of the cylinder flowing from one cylinder to the other is -View Solution
- 9The energy dissipated by a resistor is $10 \,mJ$ in $1\,s$ when an electric current of $2\, mA$ flows through it. The resistance is $....... \Omega$View Solution
(Round off to the Nearest Integer)
- 10Assertion : All electric devices shown in the circuit are ideal. The reading of each of ammeter $(a)$ and voltmeter $(V)$ is zero.View Solution
Reason : An ideal voltmeter draws almost no current due to very large resistance, and hence $(V)$ and $(a)$ will read zero.
