Question

Derive the resultant for parallel and series combination of resistances​

Answer 1

Answer:

Explanation:

SERIES COMBINATION

for series resistance R₁ and R₂ connected to a cell of voltage V₀

the current through both resistances will be same let it be I

voltage across R₁,  V₁ = IR₁

voltage across R₂,  V₂= IR₂

V₀ = V₁ + V₂

if an equivalent resistor R₀ is connected across the cell , V₀ = IR₀

IR₀ = IR₁ +IR₂

R₀ = R₁ + R₂

PARALLEL COMBINATION

Consider two resistors  R₁ and R₂ connected in parallel voltage across both will be same V₀ and current will be I₁ and I₂ respectively

I₁ = V₀/R₂

I₂ = V₀/R₂

total current = I₁ + I₂ = I₀

if an equivalent resistor R₀ is connected across the cell , I₀ = V₀/R₀

V₀/R₀ = V₀/R₂ +  V₀/R₂

1/R₀ = 1/R₁ + 1/R₂

add a circuit diagram also for both cases. hope this helps