Understanding Series Combination of Resistance

When electrical resistances are connected in series, it means they are connected end-to-end, forming a single path for the electric current to flow. This arrangement is common in various electrical circuits. Understanding the characteristics of a series combination of resistance is fundamental in current electricity.

Current in Series Circuits

In a series combination of resistance, there is only one path for the charges to flow from the positive terminal to the negative terminal of the power source. Imagine water flowing through pipes connected in a single line; the amount of water passing through any point in the pipe system must be the same. Similarly, in a series circuit, the electric current, which is the rate of charge flow, is the same at every point in the circuit and through each individual resistor.

This is a key property of any series combination of resistance.

Voltage Distribution in Series Circuits

Unlike current, the voltage across each resistance in a series combination is generally not the same. The total voltage supplied by the source is divided among the resistances in the series circuit. The voltage drop across each resistor depends on its resistance value, according to Ohm's Law, $V = IR$. Since the current ($I$) is the same through all resistors, the voltage drop ($V$) across a resistor is directly proportional to its resistance ($R$). A higher resistance will have a larger voltage drop across it. Thus, the voltage through each resistance in a series combination of resistance is typically different unless all resistances are equal.

This explains why the voltage in series is not constant across all components.

Power and Energy Considerations

The power dissipated by a resistance is given by the formulas $P = VI$, $P = I^2R$, or $P = V^2/R$. In a series circuit, while the current ($I$) is the same through each resistor, the voltage drop ($V$) and potentially the resistance ($R$) are different. Therefore, the power dissipated by each resistance ($P$) will generally be different, unless the resistances are all equal. Similarly, the energy consumed by a resistance over time ($E = Pt$) will also be different for each resistor if the power dissipated is different.

Understanding current electricity and these relationships is crucial for circuit analysis.

Analyzing the Options

Let's examine the given options in the context of a series combination of resistance:

• The current through each resistance is same. - As discussed, in a series circuit, there is a single path for current, so the current is indeed the same through all resistors. This aligns with the fundamental principle of current in series circuits.
• The voltage through each resistance is same. - This is incorrect. Voltage is divided among the resistors in a series circuit based on their resistance values.
• Power through each resistance is same. - This is incorrect. Power dissipation depends on both current (which is same) and resistance (which can be different), so power is generally different for different resistors.
• Energy consumed is same. - This is incorrect. Energy consumed depends on the power dissipated and time. Since power is generally different, energy consumed over the same time period will also be different.

Based on the properties of a series combination of resistance in current electricity, the only correct statement among the given options is that the current through each resistance is the same. This is a fundamental concept in studying electrical circuits and electrical resistance.