Question

Find maximum and minimum resistance obtained by three resistors 5 ohm, 10

ohm, 15 ohm.​

Answer 1

Concept used:

• Maximum resistance is obtained when resistances are connected in series.
• Minimum resistance is obtained when resistances are connected in parallel.

Solution:

For maximum Resistance,

R = R₁ + R₂ + R₃

➝ R = 5 Ω + 10 Ω + 15 Ω

➝ R = 30 Ω

∴ Maximum Resistance = 30 Ω

For minimum resistance,

$\sf{\dfrac{1}{R} = \dfrac{1}{R _{1}} + \dfrac{1}{R_{2} } + \dfrac{1}{R_{3} } }$

$\dashrightarrow \: \: \sf{ \dfrac{1}{R} = \dfrac{1}{5} + \dfrac{1}{10} + \dfrac{1}{15} }$

$\dashrightarrow \: \sf{ \dfrac{1}{R} = \dfrac{6 + 3 + 2}{30} }$

$\dashrightarrow \: \sf{ \dfrac{1}{R} = \dfrac{11}{30} }$

$\dashrightarrow \: \sf{R = \dfrac{30}{11} }$

∴ Minimum resistance = 2.72 Ω

Answer 2

Answer:

maximum resistance = series combination

R=R1+R2+R3

R=5+10+15

R=30ohm

minimum resistance = parallel combination

1/R=1/R1+1/R2+1/R3

1/R=1/5+1/10+1/15

1/R=6+3+2/30

1/R=11/30

R=30/11

R=2.7ohm

Explanation:

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