Answer:
Resistance of resistor A = 6.0 Ω and resistance of resistor B = 3.0 Ω
Explanation:
When the two resistors are in series, let V₁ = voltage in resistor A and R₁ = resistance of resistor A and V₂ = voltage in resistor B and R₂ = resistance of resistor B.
Given that V₁ + V₂ = 6.0 V and V₁ = 4.0 V,
V₂ = 6.0 V - V₁ = 6.0 V - 4.0 V = 2.0 V
Also, let the current in series be I.
So, V₁ = IR₁ and V₂ = IR₂
I = V₁/R₁ and I = V₂/R₂
equating both expressions, we have
V₁/R₁ = V₂/R₂
4.0 V/R₁ = 2.0 V/R₂
dividing through by 2.0 V, we have
2/R₁ = 1/R₂
taking the reciprocal, we have
R₂ = R₁/2
R₁ = 2R₂
From the parallel connection, let V₁ = voltage in resistor A and R₁ = resistance of resistor A and V₂ = voltage in resistor B and R₂ = resistance of resistor B. Since it is parallel, V₁ = V₂ = V = 6.0 V
Also, V₂ = I₂R₂ where I₂ = current in resistor B = 2.0 A and R₂ = resistance of resistor B
So, R₂ = V₂/I₂
= 6.0 V/2.0 A
= 3.0 Ω
R₁ = 2R₂
= 2(3.0 Ω)
= 6.0 Ω
So, resistance of resistor A = 6.0 Ω and resistance of resistor B = 3.0 Ω
