Many resistors connected in series will?

Question

Examoogle · Accepted Answer

Divide the voltage proportionally among all the resistors

Explanation: In a series circuit, resistors are connected end-to-end, creating a single path for current flow. According to Kirchhoff's Voltage Law (KVL), the total supply voltage is distributed across each resistor in direct proportion to its resistance value.

Working Principle: Since the same current $I$ flows through every resistor in series, the voltage drop $V_k$ across a resistor $R_k$ is calculated by $V_k = I \cdot R_k$. Because $I$ is constant throughout the series branch, the voltage drop is directly proportional to the resistance value ($V \propto R$), causing larger resistors to drop more voltage.

Key Formulas: $V_k = I \cdot R_k$ — Voltage drop across the k-th resistor; $V_{total} = \sum V_k = I \cdot \sum R_k$ — Kirchhoff's Voltage Law

Key Points: The current flowing through all series resistors is identical ($I_{total} = I_1 = I_2 = ... = I_n$).; The sum of all individual voltage drops equals the applied source voltage.; Resistors in series act as a voltage divider circuit.

Advantages: Provides a simple method to reduce voltage levels for specific components.; Easier to calculate total resistance (additive).

Disadvantages: If one resistor fails (open circuit), the entire path is broken.; Voltage across individual components depends on the values of other series resistors.

Applications: Potentiometers and rheostats.; Bias circuitry in transistor amplifiers.; Sensor interface circuits.

Additional Info: Option B is incorrect because current remains constant in series, not divided.. Option C is incorrect because resistors dissipate power, they do not act as voltage sources to increase supply.. Option D is incorrect as the circuit consumes power rather than eliminating it.

Answer: A is correct — resistors in series function as a voltage divider, where the supply voltage is distributed proportionally among them based on Ohm's Law.

Exam Tip: Remember: In series, current is common (constant) and voltage is shared (divided). In parallel, voltage is common and current is shared (divided).

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