Resistors in Series vs. Parallel: Key Differences Explained

This article clarifies the differences between resistors connected in series and resistors connected in parallel. We’ll explore how current, voltage, and equivalent resistance behave in each configuration.

Resistors in Series

resistors in series

When resistors are connected in series, as shown in the figure above, we can derive the following principles. These principles apply regardless of the number of resistors in the series.

• Current Flow (I): The current (I) is the same through all resistors in a series circuit.
• Voltage: The voltage drop across each individual resistor depends on its resistance value (Ohm’s Law: $V = I * R$).
• Total Voltage: The total voltage ($V$) across the entire series combination is the sum of the voltage drops across each individual resistor. So, $V = V_1 + V_2$, which translates to $I * R = I * R_1 + I * R_2$.
• Total Resistance (Equivalent Resistance): The total or equivalent resistance ($R$) of resistors in series is simply the sum of the individual resistance values.
• For two resistors in series: $R = R_1 + R_2$.
• SI Unit: The SI unit for resistance is the Ohm (Ω).

Resistors in Parallel

resistors in parallel

When resistors are connected in parallel, as shown in the figure, different rules apply:

• Voltage: The voltage across all resistors in a parallel circuit is the same.
• Total Current: The total current ($I$) entering the parallel combination is the sum of the currents flowing through each individual resistor. Thus, $I = I_1 + I_2$, which can be expressed as $V/R = V/R_1 + V/R_2$.
• Total Resistance (Equivalent Resistance): Calculating the total resistance for resistors in parallel requires a different approach.
  • For two resistors in parallel: $1/R = 1/R_1 + 1/R_2$, which can be rearranged to $R = (R_1 * R_2) / (R_1 + R_2)$.
  • For multiple resistors in parallel: $1/R = 1/R_1 + 1/R_2 + 1/R_3 + ... + 1/R_n$, where n is the total number of resistors.

The choice between series and parallel resistor configurations depends entirely on the specific requirements of the electronic circuit design.

Summary Table: Series vs. Parallel Resistors

Circuit Type	Resistors in Series	Resistors in Parallel
Schematic Diagram
Current	$I = I_1 = I_2 = I_3 ...$ = Same for each resistor	$I = I_1 + I_2 + I_3 ...$ = Sum of currents
Potential Difference	$ΔV = ΔV_1 + ΔV_2 + ΔV_3 ...$ = Sum of potential differences	$ΔV = ΔV_1 = ΔV_2 = ΔV_3 ...$ = Same for each resistor
Equivalent Resistance	$R_{eq} = R_1 + R_2 + R_3 ...$ = Sum of individual resistances	$(1/R_{eq}) = (1/R_1) + (1/R_2) + (1/R_3) + ...$ = Reciprocal sum of resistances