19 Two resistors of R1 ohms and R2 ohms are connected in series to a battery which has an e.m.f. of V.

Which formula gives the power dissipated by resistor R1?

Answer:

19) D

Total resistance of the circuit = R₁ + R₂
Voltage = V

We know current remains the same across both resistors.
Current of circuit (I) = V ÷ (R₁ + R₂)

We know V = IR
Voltage across R₁ (V₁) = I x R₁
V₁ = [V÷ (R₁ + R₂)] x R₁ = VR₁ ÷ (R₁ + R₂)

We know P = VI
Power across R₁ = V₁ x I
P₁ = [VR₁ ÷ (R₁ + R₂)] x [V ÷ (R₁ + R₂)]
P₁ = V²R ÷ (R₁ + R₂)²

Hence the answer is D.