The circuit diagram shown consists of a large number of element (each element has two resistors $R_1$ and $R_2$). The resistance of the resistors in each subsequent element differs by $a$ factor of $K = 1/2$ from the resistance of the resistors in the previous elements. The equivalent reistance between $A$ and $B$ shown in figure is :
Advanced
Download our app for free and get started
When each element of circuit is multiplied by a factor $k$ then equivalent resistance also become $k$ times.
Let the equivalent resistance between $A$ and $B$ be $X$
So, equivalent circuit becomes
For $k=\frac{1}{2}$
$\Rightarrow \mathrm{X}=\frac{\left(\mathrm{R}_{1}-\mathrm{R}_{2}\right)+\sqrt{\mathrm{R}_{1}^{2}+\mathrm{R}_{2}^{2}+6 \mathrm{R}_{1} \mathrm{R}_{2}}}{2}$
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 resistance of a wire is $R\; ohm$. If it is melted and stretched to $'n'$ times its original length, its new resistance will beView Solution
- 2On giving $220\,V$ to a resistor the power dissipated is $40\,W$ then value of resistance is ............... $\Omega$View Solution
- 3One $kg$ of water, at $20\,^oC$, is heated in an electric kettle whose heating element has a mean (temperature averaged) resistance of $20\, \Omega $. The rms voltage in the mains is $200\, V$. Ignoring heat loss from the kettle, time taken for water to evaporate fully, is close to.......... $\min$ [Specific heat of water $= 4200\, J/kg\, ^oC$), Latent heat of water $= 2260\, k\,J/kg$]View Solution
- 4Find charge on the capacitor after $1$ sec of opening the switch at $t=\infty ?$View Solution
- 5Two wires $A$ and $B$ are made up of the same material and have the same mass. Wire A has radius of $2.0 \mathrm{~mm}$ and wire $B$ has radius of $4.0 \mathrm{~mm}$. The resistance of wire B is $2 \Omega$. The resistance of wire $\mathrm{A}$ is_______. $\Omega$.View Solution
- 6An infinite line charge of uniform electric charge density i. lies along the axis of an electrically conducting infinite cylindrical shell of radius $R$. At time $t=0$, the space inside the cylinder is filled with a material of permittivity $\varepsilon$ and electrical conductivity $\sigma$. The electrical conduction in the material follows Ohm's law. Which one of the following graphs best describes the subsequent variation of the magnitude of current censity $j(t)$ at any point in the material?View Solution
- 7Two wires $A$ and $B$ of the same material, having radii in the ratio $1: 2$ carry currents in the ratio $4: 1$. The ratio of drift speed of electrons in $A$ and $B$ is .......View Solution
- 8The potential at point $E$ for the given figure is ................ $\mathrm{V}$View Solution
- 9View SolutionThe relaxation time in conductors
- 10For a cell of $e.m.f.$ $2\,V$, a balance is obtained for $50\, cm$ of the potentiometer wire. If the cell is shunted by a $2\,\Omega $ resistor and the balance is obtained across $40\, cm$ of the wire, then the internal resistance of the cell is ............. $\Omega $View Solution