Explanation:
Ohm's law describes the relationship between voltage, current, and resistance.
V = IR
where V is voltage, I is current, and R is resistance.
A. At the original voltage:
V₁ = I₁ R₁
When the voltage is doubled and resistance stays the same:
2V₁ = I₁' R₁
Dividing the two equations:
2V₁ / V₁ = (I₁' / I₁) (R₁ / R₁)
2 = I₁' / I₁
So the new current is double the original current.
B. At the original voltage and resistance:
V₂ = I₂ R₂
When both the voltage and resistance are increased by a factor of 2:
2V₂ = I₂' (2R₂)
Dividing the two equations:
(2V₂ / V₂) = (I₂' / I₂) (2R₂ / R₂)
2 = (I₂' / I₂) (2)
1 = I₂' / I₂
So the new current is the same as the original current.
