In a series combination of resistors, how is the voltage distributed across each resistor?

Question

Examoogle · Accepted Answer

The correct answer is Option D: Directly proportional to resistance. In a series circuit, the current flowing through each resistor is identical because there is only one continuous path for charge flow. According to Ohm's Law ($V = I 	imes R$), since current $I$ is constant, the potential difference (voltage drop) across any individual resistor $V_x$ is directly proportional to its resistance $R_x$.

Step-by-Step Solution & Concepts:
In a series circuit, the current flowing through each resistor is identical because there is only one continuous path for charge flow. According to Ohm's Law ($V = I 	imes R$), since current $I$ is constant, the potential difference (voltage drop) across any individual resistor $V_x$ is directly proportional to its resistance $R_x$.

Working Principle: In a series circuit containing $n$ resistors, the total equivalent resistance is $R_{eq} = R_1 + R_2 + \dots + R_n$. By Ohm's Law, the total circuit current is $I = \frac{V_{total}}{R_{eq}}$. The voltage drop across a specific resistor $R_x$ is given by $V_x = I 	imes R_x = V_{total} 	imes \left(\frac{R_x}{R_{eq}}ight)$, which explicitly shows that voltage drop is directly proportional to resistance.

Key Formulas: $V = I 	imes R$ — Ohm's Law; $V_x = V_{total} 	imes \left(\frac{R_x}{R_{eq}}ight)$ — Voltage Divider Rule for Series Combination; $V_{total} = V_1 + V_2 + \dots + V_n$ — Kirchhoff's Voltage Law (KVL) in Series

Key Points: In a series combination, the current ($I$) remains identical through all resistors.; The total voltage of the source equals the sum of voltage drops across each resistor: $V = V_1 + V_2 + \dots + V_n$.; Resistors with higher resistance develop larger voltage drops across them.; The equivalent resistance in series is the sum of individual resistances ($R_{eq} = R_1 + R_2 + \dots + R_n$).

Advantages: Simple circuit configuration with a single current path.; Acts as an efficient voltage divider circuit to drop voltage levels safely.

Disadvantages: If one component fails or breaks open, the current stops completely across the entire circuit.; Adding more resistors increases total resistance, reducing overall circuit current.

Applications: Decorative Christmas tree fairy lights connected in series.; Voltage divider networks used in sensor interfaces and electronics.

Additional Info: Option A describes a parallel combination where voltage is the same across all components.. Option B is incorrect because voltage drop directly depends on resistance value via $V = I 	imes R$.. Option C describes current distribution in a parallel circuit ($I \propto \frac{1}{R}$).

Answer: D is correct — In a series circuit, current remains constant across all components, making the voltage drop directly proportional to resistance according to Ohm's Law ($V \propto R$).

Exam Tip: Remember: Series = Current Constant ($V \propto R$), Parallel = Voltage Constant ($I \propto \frac{1}{R}$). Keep this rule handy for numerical problems in SSC and RRB physics exams.

Examoogle · Answer

Option A: The same across all resistors

Examoogle · Answer

Option B: Unaffected by resistance values

Examoogle · Answer

Option C: Inversely proportional to resistance

Feature	Series Combination	Parallel Combination
Current (I)	Same through all resistors	Divides among parallel branches
Voltage Drop (V)	Directly proportional to resistance ( $V \propto R$ )	Same across all parallel branches
Equivalent Resistance	$R_{eq} = R_1 + R_2 + \dots$	$\frac{1}{R_{eq}}$ = $\frac{1}{R_1}$ $+ \frac{1}{R_2}$ + \dots

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