The sum of the voltage drops in a series circuit is equal to the
The Correct Answer and Explanation is:
In a series circuit, the sum of the voltage drops across all components is equal to the total voltage supplied by the source. This is known as Kirchhoff’s Voltage Law (KVL), which states that the total voltage around any closed loop or circuit is zero.
Explanation:
In a series circuit, the same current flows through all components, but each component (such as resistors, light bulbs, or other loads) causes a voltage drop according to Ohm’s Law, which is:
[
V = I \times R
]
Where:
- V is the voltage drop across the component,
- I is the current flowing through the component,
- R is the resistance of the component.
Since the current is the same throughout a series circuit, the voltage drops depend on the individual resistances of each component. The total voltage provided by the power source is divided among the components in proportion to their resistances.
Kirchhoff’s Voltage Law:
According to Kirchhoff’s Voltage Law, in any closed loop, the sum of all the voltages around the loop must equal zero. This means that the sum of the voltage drops across all components in a series circuit will be equal to the total voltage supplied by the power source.
Mathematically, this can be expressed as:
[
V_{total} = V_1 + V_2 + V_3 + \dots + V_n
]
Where:
- V_total is the total voltage supplied by the source,
- V_1, V_2, …, V_n are the individual voltage drops across each component.
Thus, the voltage supplied by the battery or power source is distributed among the components, and the sum of these individual voltage drops is always equal to the total voltage.
Example:
Consider a simple series circuit with a 12V battery and three resistors. If the voltage drop across the first resistor is 4V, across the second is 5V, and across the third is 3V, then:
[
4V + 5V + 3V = 12V
]
This confirms that the total voltage (12V) is the sum of the individual voltage drops in the series circuit.