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When several resistors are joined in series, the equivalent resistance of the combination is:
greater than the sum of the individual resistances
equal to the sum of the individual resistances
less than the sum of the individual resistances
equal to the product of the individual resistances
equal to the sum of the individual resistances
When resistors are connected in series, the same current flows through each resistor, and the total potential difference across the combination is the sum of the potential differences across each individual resistor. Consequently, the equivalent resistance (RsтАЛ) is equal to the sum of the individual resistances (R1тАЛ+R2тАЛ+...+RnтАЛ).
When resistors are connected in series, the same current flows through each resistor, and the total potential difference across the combination is the sum of the potential differences across each individual resistor. Consequently, the equivalent resistance (RsтАЛ) is equal to the sum of the individual resistances (R1тАЛ+R2тАЛ+...+RnтАЛ).
Think of resistors in series like adding more obstacles in a single water pipe; the total length of the pipe (resistance) increases as you add more segments, making it harder for water (current) to flow.
SUM = Series, United, Mostly-additive
RsтАЛ=R1тАЛ+R2тАЛ+...+RnтАЛ тАФ Sum of individual resistances in series
V=I├ЧR тАФ Ohm's Law relationship
In a series circuit, Ohm's law states V=I├ЧR. Since the current I is constant throughout the series path, the total voltage VtotalтАЛ=V1тАЛ+V2тАЛ+...+VnтАЛ. Substituting V=I├ЧR into this equation gives I├ЧRsтАЛ=I├ЧR1тАЛ+I├ЧR2тАЛ+...+I├ЧRnтАЛ. By canceling I from both sides, we arrive at the additive property of resistance.
The total resistance in a series circuit is always greater than any individual resistance.
The same amount of current flows through every component in a series circuit.
The total voltage of the circuit is distributed across the resistors proportional to their resistance values.
Simple to design and implement for voltage division.
The total resistance value is increased, which can be useful to limit current flow.
If one component fails, the entire circuit path is broken (open circuit).
Not suitable for household wiring where independent device control is required.
Used in potential divider circuits.
Used in Christmas light strings (older versions where one bulb out turns off the whole string).
Option A is incorrect because the resistance is exactly equal, not greater than the sum.
Option C is incorrect as the sum is only less than individual values in parallel connections.
Option D is incorrect as products are not used for calculating equivalent resistance in series.
B is correct тАФ When resistors are joined in series, the equivalent resistance is equal to the sum of the individual resistances.
Always remember that in parallel circuits, the reciprocal of the equivalent resistance is the sum of the reciprocals: RpтАЛ1тАЛ=R1тАЛ1тАЛ+R2тАЛ1тАЛ+...
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