Combination of Resistors

The equivalent capacitance across $A \& B$ is

Write steady state current in the $2 \Omega$ resistor shown in the circuit (see figure). The internal resistance of the battery is negligible and the capacitance of the condenser $C$ is $0.2 \mathrm{mF}$ is terms of $N\times {10}^{-1}\mathrm{amp}$.

A hemisphere network of radius '$a$' is made by using a conducting wire of resistance per unit length $r$. Find the equivalent resistance across $OP$.

A piece of resistive wire is made up into two squares with a common side of length $10 \mathrm{cm}$. A current enters th rectangular system at one of the corners and leaves at the diagonally opposite corners. Show that the current in the common side is $\frac{1}{5}$ th of the entering current. What length of wire connected between input and output terminals would have an equivalent effect.

A triangle is constructed using the wires $AB,BC\&CA$ of same material and of resistance $\alpha ,2\alpha \&3\alpha$ respectively, Another wire of resistance $\frac{\alpha }{3}$ from A can make a sliding contact with wire $BC$. Find the maximum resistance of the network between points $A$ and the point of sliding wire with $BC$.

In the circuit shown in figure, all wires have equal resistance $r$. Find the equivalent resistance between $A$ and $B$.

A network of nine conductors connects six points $A, B, C, D, E$ and $F$ as shown in figure. The figure denotes resistances in ohms. Find the equivalents resistance (in ohm) between $A$ and $D$.

Find the effective resistance of the network (see figure) between the points $A$ and $B$ where $R=1\Omega$ is the resistance of each part.

The figure shows a network of resistor each heaving value $12\Omega$.Find the equivalent resistance between points $A$ and $B$ (in ohm).

In the circuit shown in figure, calculate the current (in $A$ ) through $S$ in the circuit when $S$ is closed.

Find the current through $25 \mathrm{V}$ cell (in $A$ ) in the figure shown.

At what value of the resistance $R_x$ in the circuit shown in figure will the total resistance between points $A$and $B$ be independent of the number of loops? [Given : $R=(\sqrt{3}+1)$]

Find current in the branch $CD$ of the circuit (in ampere).

In given electrical circuit, let power supplied by battery $E_1$ be '$a$' watt and power supplied by battery $E_2$ ? be ' $b$ ' watt then what is the value of $a+b$.

Find the resistor in which maximum heat will be produced.

 Consider an infinte ladder network shown in figure. A voltage $V$ is applied between the points $A$ and $B$. This applied value of voltage is halved after each section.
  

In the diagram resistance between any two junctions is $R$. Equivalent resistance across terminals $A$ and $B$ is

$ABCD$ is a square where each side is a uniform wire of resistance $1\mathrm{\Omega }$. A point $E$ lies on $CD$ such that if a uniform wire of resistance $1\mathrm{\Omega }$ is connected across $AE$ and constant potential difference is applied across $A$ and $C$ then $B$ and $E$ are equipotential : 

In the box shown current $i$ enters at $H$ and leaves at $C$. If $i_{AB}=\frac{i}{6},i_{DC}=\frac{2i}{3},i_{HA}=\frac{i}{2},i_{GF}=\frac{i}{6},i_{HE}=\frac{i}{6}$ choose the branch in which current is zero
 

 Consider the circuit shown in the figure