Questions: Resistor Combinations and Equivalent Resistance

Question 1

You add a third resistor in parallel to two existing parallel resistors in a circuit. What happens to the equivalent resistance of the parallel combination?

• A. It increases, because you are adding more total resistance to the circuit
• B. It stays the same, because parallel resistors are electrically independent
• C. It decreases, because you have opened an additional path for current to flow
• D. It depends on whether the new resistor is larger or smaller than the existing ones

Answer: (C)

Adding any resistor in parallel always decreases the equivalent resistance, regardless of its value. The formula 1/R_eq = 1/R₁ + 1/R₂ + 1/R₃ shows that each new term increases 1/R_eq, which means R_eq decreases. The physical reason: another parallel branch provides another current pathway. The total current the source must supply increases, which means the effective load seen by the source is smaller. Option A is the classic misconception from confusing series and parallel behavior.

Question 2

Two resistors R₁ = 4Ω and R₂ = 4Ω are connected in series across a 12V battery. What is the current through R₂?

• A. 3A — applying Ohm's law directly to R₂: V/R₂ = 12V / 4Ω
• B. 1.5A — the total current through the series circuit: 12V / (4Ω + 4Ω)
• C. 6A — total voltage divided by the smallest resistor
• D. 0.75A — half the series current, since the resistors are identical

Answer: (B)

In a series circuit, there is only one path for current. The same current flows through every element — both resistors and the battery. The total equivalent resistance is 4 + 4 = 8Ω, so the current is 12V / 8Ω = 1.5A. Option A is the trap: using the full 12V with just R₂ would be correct if R₂ were the only element, but in series, 12V is shared across both resistors (6V each). Option D confuses series current (which is the same everywhere, not split) with parallel current.

Question 3

In a parallel circuit, if one branch's resistor is replaced with a larger one, the voltage across all other branches remains unchanged.

• T. True
• F. False

Answer: True

In a parallel circuit, all branches connect between the same two nodes — they all share the same terminal voltage. Changing one branch's resistor changes the current through that branch, but does not change the voltage that the source maintains across the parallel combination (assuming an ideal voltage source). This is why household appliances in parallel don't affect each other's voltage: each is independently connected to the same supply rails.

Question 4

Adding resistors in series decreases the total equivalent resistance because each additional resistor provides another path for current.

• T. True
• F. False

Answer: False

This describes parallel, not series. In series, there is only one path — adding more resistors in series lengthens that single path, increasing total resistance: R_eq = R₁ + R₂ + R₃ + ... Adding resistors in PARALLEL decreases resistance by providing additional current paths. Confusing these two is extremely common because both involve 'adding' resistors — the key distinction is whether you are adding more obstacles on the same path (series) or more alternative paths (parallel).

Question 5

What is the key question to ask when identifying whether resistors are in series or parallel, and why does the answer determine which formula to use?

Model answer: The key question is: do these resistors carry the same current, or do they share the same voltage? If the same current flows through all of them (only one path), they are in series: R_eq = R₁ + R₂ + ... If they all connect between the same two nodes (same voltage), they are in parallel: 1/R_eq = 1/R₁ + 1/R₂ + ... These two topologies produce opposite effects on equivalent resistance — series always increases it, parallel always decreases it.

This question — shared current or shared voltage? — is the fundamental diagnostic for circuit simplification. It applies recursively to complex networks: identify a sub-group that clearly shares a current path (series) or shares two nodes (parallel), reduce it, and repeat. The physical insight behind each formula flows directly from the answer: series obeys voltage addition (drops add along one path); parallel obeys current addition (currents split at a node).