How do series and parallel resistor networks differ in their equivalent resistance?

How do series and parallel resistor networks differ in their equivalent resistance?

• A. Series: R_eq = sum R; current is the same through all; Parallel: 1/R_eq = sum (1/R_i); voltage is the same across all.
• B. Series: R_eq = product of R; parallel: 1/R_eq = sum (1/R_i); current is different through each.
• C. Series: R_eq = 1 / sum (1/R_i); parallel: R_eq = sum R_i; voltage varies across components.
• D. Series: R_eq = sum R; current varies; Parallel: R_eq = sum R_i; voltage varies.

Answer: (A)

When resistors are in series, they behave like one longer resistor: the total resistance is simply the sum of each resistor, and the same current flows through every component because there’s only one path for the current. When resistors are in parallel, the voltage across each branch is the same (since all branches are connected to the same two nodes), the currents in the branches add up to the total, and the equivalent resistance is found from the reciprocal rule: 1/R_eq = sum(1/R_i). For two resistors in parallel, that gives R_eq = (R1*R2)/(R1+R2). This combination of ideas is why the description states series resistances add and current stays the same, while for parallel the reciprocal sum rule applies and the voltage is the same across all branches. Other statements mix up these relationships (like claiming the series resistance multiplies, or the parallel resistance simply adds, or that voltage varies across parallel branches), which doesn’t match how series and parallel networks actually behave.

When resistors are in series, they behave like one longer resistor: the total resistance is simply the sum of each resistor, and the same current flows through every component because there’s only one path for the current. When resistors are in parallel, the voltage across each branch is the same (since all branches are connected to the same two nodes), the currents in the branches add up to the total, and the equivalent resistance is found from the reciprocal rule: 1/R_eq = sum(1/R_i). For two resistors in parallel, that gives R_eq = (R1*R2)/(R1+R2). This combination of ideas is why the description states series resistances add and current stays the same, while for parallel the reciprocal sum rule applies and the voltage is the same across all branches. Other statements mix up these relationships (like claiming the series resistance multiplies, or the parallel resistance simply adds, or that voltage varies across parallel branches), which doesn’t match how series and parallel networks actually behave.