Question

the maximum resistance which can be made using
four resistors each of resistance 1/2 ohm is
options :-
(a) 2 ohms
(b)
1 ohms
(c)
2.5
ohm
s
(d) 8ohms​

Answer 1

Given :

Four resistors each of resistance 1/2 Ω i.e.,

• R₁ = 1/2 ohms
• R₂ = 1/2 ohms
• R₃ = 1/2 ohms
• R₄ = 1/2 ohms

To find :

The maximum resistance of the resistors connection.

Solution :

The maximum resistance can be obtained when it is connected in series.

» The combined resistance of any number of resistance connected in series is equal to the sum of the individual resistances. i.e.,

$\boxed{\bf R_{max} = R_1 + R_2 + R_3 + R_4}$

By substituting the values,

$\dashrightarrow\sf R_{max} = R_1 + R_2 + R_3 + R_4$

$\dashrightarrow\sf R_{max} = \dfrac{1}{2} + \dfrac{1}{2} + \dfrac{1}{2} + \dfrac{1}{2}$

$\dashrightarrow\sf R_{max} = \dfrac{1 + 1 + 1 + 1}{2}$

$\dashrightarrow\sf R_{max} = \dfrac{4}{2}$

$\dashrightarrow\sf R_{max} = 2 \: ohms$

Thus, the maximum resistance obtained is 2 ohms.

Hence, option (a) 2 ohms is correct.

Remember !

SI unit of resistance is ohms.

Answer 2

Given :-

Four resistors each of resentence 1/2 Ω i.e.,

• ${\sf{R_{1} }}$ = 1/2 ohms
• ${\sf{R_{2}}}$ = 1/2 ohms
• ${\sf{R_{3}}}$ = 1/2 ohms
• ${\sf{ R_{4}}}$ = 1/2 ohms

To find :-

• The maximum resistance of the resistors connection.

Solution :-

The maximum resistance can be obtained when it is connected in series.

➝The combination resistance of any number of resistance connected in series is equal to the sum of the individual resistance. i.e.,

${\bf\green{★}}$ $\boxed{\bf{R_{max} = R_{1} + R_{2} + R_{3} + R_{4}}}$ ${\bf\red{★}}$

By substituting the values ,

$\implies\bf$ ${\sf{R_{max} = R_{1} + R_{2} + R_{3} + R_{4}}}$

$\implies\bf$ ${\sf{R_{max} = \frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2} }}$

$\implies\bf$ ${\sf{R_{max} = \frac{1 \: + 1 \: + 1 \: + 1}{2} }}$

$\implies\bf$ ${\sf{R_{max} = \frac{4}{2} }}$

$\implies\bf$ ${\sf{R_{max} = 2 \: ohms}}$

Thus, the maximum resistance obtained is 2 ohms.

Hence,

• Option (a) 2 ohms $\large{\bf\green{✓}}$ is correct.

Remember :

• Sl unit is resistance is ohms.