Question

Question Number 5 Answer

Answer 1

Answer:

R eq = 3.33 ohm

Solution :

please refer the attachment for better understanding

Step 1 : Draw a line of symmetry

Step 2 : Fold the symmetrical part as shown in fig B and then double the resistance

Fig B :

Between A and C :

Two resistors of each of resistance 6 ohm are connected in series

Equivalent resistance for the resistors connected in series is given by the formula,

$\implies \mathtt{R_s = R_1 + R_ 2}$

here ,

• R 1 = R 2 = 6 ohm

$\implies \mathtt{R_s = 6 + 6}$

$\implies \mathtt{R_s = 12 \: ohm}$

This 12 ohm resistor is in parallel with 6 ohm resistor

Equivalent resistance for the resistors connected in parallel is given by the formula,

$\implies \mathtt{ \dfrac{1}{R_p} = \dfrac{1}{R_1} + \dfrac{1}{R_2} }$

here ,

• R 1 = 12 ohm
• R 2 = 6 ohm

$\implies \mathtt{ \dfrac{1}{R_p} = \dfrac{1}{12} + \dfrac{1}{6} }$

$\implies \mathtt{ \dfrac{1}{R_p} = \dfrac{1 + 2}{12} }$

$\implies \mathtt{ R_p= \dfrac{12}{3} }$

$\implies \mathtt{ R_p=4 \: ohm}$

______________________

Between A and B :

Two resistors of resistance 4 ohm and 6 ohm respectively are connected in series

Equivalent resistance for the resistors connected in series is given by the formula,

$\implies \mathtt{R_s = R_1 + R_ 2}$

here ,

• R 1 = 4 ohm
• R 2 = 6 ohm

$\implies \mathtt{R_s = 4 + 6}$

$\implies \mathtt{R_s =10 \: ohm}$

This 10 ohm resistor is in parallel with 5 ohm resistor

Equivalent resistance for the resistors connected in parallel is given by the formula,

$\implies \mathtt{ \dfrac{1}{R_p} = \dfrac{1}{R_1} + \dfrac{1}{R_2} }$

here ,

• R 1 = 10 ohm
• R 2 = 5 ohm

$\implies \mathtt{ \dfrac{1}{R_p} = \dfrac{1}{10} + \dfrac{1}{5} }$

$\implies \mathtt{ \dfrac{1}{R_p} = \dfrac{1 + 2}{10} }$

$\implies \mathtt{ R_p = \dfrac{10}{3} }$

$\implies \mathtt{ R_p =3.33 \: ohm}$

The equivalent resistance of the circuit is 3 .33 ohm