Question

A network of nine conductors connects six points A, B, C, D, E, and F as shown below.

The digit denotes the resistance in ohm. Find the equivalent resistance between A and D.

Answer 1

Resistors are connected in series whenever the current flows through the resistors equally. Resistors are connected to one another through a continuous wire of small resistance is known as parallel resistance.
The equivalent resistance of resistors in a series connection is the algebraic sum of the individual resistances

Complete step by step solution:
The equivalent resistance combination of resistors depends on their values and how they are connected. The easiest combinations of resistors are series and parallel connections. In a series circuit, the output current of the first resistor is given to the input of the second resistor; here, the current is the same in each resistor.
In a parallel circuit, the resistor leads on one side of the resistors are connected together and all the leads on the other side are connected.
Let voltage at A be ${V_A}$
Let current from A to B is ${i_{AB}}$
Now,
${V_B} = {V_A} - {i_{AB}}({R_{AB}})$
Now,
$= {V_A} - {i_{AB}}$
Similarly,
${V_C} = {V_A} - {i_{AC}}$
Now,
${i_{AC}} = {i_{AB}}$
Here, ${V_B} = {V_C}$
${i_{BC}} = 0$
Now, the resultant circuit is,

$\dfrac{1}{{{\operatorname{R} _{eff}}}} = \dfrac{1}{2} + \dfrac{1}{{1 + 2 + 1}} + \dfrac{1}{{1 + 2 + 1}}$
Here, the effective resistance is,
$\dfrac{1}{{{\operatorname{R} _{eff}}}} = 1$
$\operatorname{R} _{eff} = 1$
Here the equivalent resistance between AD is, $1\Omega$

Note: The voltage drop is the same across every parallel branch.
The sum of the current individual branch is the same as the current at the outside of the branches In the parallel circuit, each resistor has an equal potential drop across it, and the currents through every resistor may be different, depending on the resistor.