Question

Because the resistor and capacitor are connected in series, the sum of the resistor voltage and the capacitor voltage must equal the voltage of the power source at each point in time.

Option 1: True, because in a series circuit, the voltages across individual components add up to the total voltage.
Option 2: False, because in a series circuit, the voltage across the resistor and the capacitor may not always equal the voltage of the power source.
Option 3: True, because in a series circuit, the voltages across individual components are always equal to the voltage of the power source.
Option 4: False, because the relationship between the voltages in a series circuit depends on the values of the resistor and capacitor, and they may not always sum to the power source voltage.

Answer 1

In a series circuit, it is true that the sum of the voltages across individual components like resistors and capacitors equals the total voltage of the power source, because the circuit must obey the principle of energy conservation.

The correct option is option 1.

Step-by-step explanation:

The student asked whether in a series circuit, the sum of the resistor voltage and the capacitor voltage will always equal the voltage of the power source. The correct answer to this is Option 1: True, because in a series circuit, the voltages across individual components add up to the total voltage supplied by the power source.

We know this because every resistor and capacitor connected in series with the power source will share the same current. According to Ohm's law, the voltage drop across each component is the product of the current and the resistance (V = IR). In a series circuit, energy is conserved and the sum of these voltage drops must equal the total supplied voltage.

The individual voltage drops across a series circuit depend on the resistance of each component. The total resistance of a series circuit is the sum of individual resistances (Rs = R1 + R2 + ...) and the same current flows through each component.

Resistor voltage and capacitor voltage are different types of potential drops; the resistor voltage is due to resistance, while the capacitor voltage is due to electric field storage. Despite this difference, their combined voltages at any instant still add to reflect the total voltage from the power source.

The correct option is option 1.