Question

The total power taken from the power supply and dissipated by the resistors in a series circuit is equal to the sum of the powers dissipated by each resistor in the circuit.a. Trueb. False

Answer 1

a) True.

Step-by-step explanation:

In a series circuit, the voltage through any resistor, can be expressed using Ohm´s Law, as follows:

Vr = I * R

In a series circuit, the current is the same at any point in the circuit, and can be expressed as follows (applying Ohm´s Law):

I = V / (R₁ + R₂ + ....+ Rₙ)

So, the power dissipated at any resistor can be expressed as follows:

Pr = Vr*I = (V/ (R₁ + R₂ + ....+ Rₙ))*Rₙ*I

If we add the n powers, we finally arrive at the following equation:

Pt = (R₁+R₂+....+Rₙ)/(R₁ + R₂ + ....+ Rₙ)* V*I = V*I

But the product V*I, is just all the power taken from the power supply, so, it is equal to the sum of the powers dissipated by each resistor.

This means that there is no power absorbed at any point of the circuit.