Question

Two resistance of 4? and 8? are connected in parallel. What is the combined
resistance of the system?

Answer 1

Given

• Two resistors are connected in parallel
• R₁ = 4Ω
• R₂ = 8Ω

To Find

• Equivalent resistance

Solution

● Then equivalent resistance of a parallel combination is given by, 1/Rₙₑₜ = 1/R₁ + 1/R₂ ... + 1/Rₙ

✭ Equivalent Resistance :

→ 1/Rₙₑₜ = 1/R₁ + 1/R₂ ... + 1/Rₙ

• R₁ = 4Ω
• R₂ = 8Ω

→ 1/Rₙₑₜ = 1/4 + 1/8

→ 1/Rₙₑₜ = (1/4 × 2/2) + 1/8

→ 1/Rₙₑₜ = 2/8 + 1/8

→ 1/Rₙₑₜ = (2+1)/8

→ 1/Rₙₑₜ = 3/8

→ Rₙₑₜ = 8/3

→ Rₙₑₜ = 2.7 Ω

Answer 2

Given:-

☆Two resistance if 4 ohm and 8 ohm are connected in parallel

To Find:-

☆Combined resistance of the system...?

Solution:-

☆We Know,

$\leadsto{ \boxed{ \boxed{ \boxed{ \bold{ \frac{1}{R _n \: _e \:_t } = \frac{1}{R _1 } + \frac{1}{R_2} }}}}}$

$\leadsto{ \boxed{ \boxed{ \boxed{ \bold{ \frac{1}{R _n \: _e \:_t } = \frac{1 \times 2}{4 \times 2} + \frac{1}{8} }}}}}$

$\leadsto{ \boxed{ \boxed{ \boxed{ \bold{ \frac{1}{R _n \: _e \:_t } = \frac{2}{8} + \frac{1}{8} }}}}}$

$\leadsto{ \boxed{ \boxed{ \boxed{ \bold{ \frac{1}{R _n \: _e \:_t } = \frac{3}{8}}}}}}$

$\leadsto{ \boxed{ \boxed{ \boxed{ \bold</u><u>{</u><u>\</u><u>red</u><u>{ \frac{1}{R _n \: _e \:_t } = 2.7 \: ohm}}</u><u>}</u><u>}}}$

☆Hence combined resistance of the system is 2.7 ohm..