Does adding a resistor always increase the total resistance?
Short answer: Parallel adds new paths, so total resistance drops: 1/R_total = 1/R + 1/R.
The trap
The wrong idea
“Adding a resistor always increases the total resistance.”
It sounds reasonable, and a lot of JEE/NEET aspirants carry it into the exam. Here's a one-question check, then the explanation that makes it click.
Quick check
Try it before you peek
Adding a second identical resistor in PARALLEL to one resistor R makes the total:
- 2R
- R/2
- R
Show the answer
B. R/2
Parallel adds new paths, so total resistance drops: 1/R_total = 1/R + 1/R.
The click
It depends on how you connect it. In series, resistances add: R_total = R₁ + R₂, so adding a resistor always increases the total. In parallel, the reciprocals add: 1/R_total = 1/R₁ + 1/R₂, and adding a resistor always decreases the total.
For two identical resistors R in parallel, 1/R_total = 1/R + 1/R = 2/R, so R_total = R/2. More generally, a parallel combination is always smaller than the smallest single resistor in it.
Why? A parallel resistor adds a new path for the current. With the same voltage V across the combination, each branch carries its own current V/R, so the total current doubles while V stays the same, and R_total = V/I halves. Think of opening a second checkout counter in a shop: the queue clears faster even though each counter is just as slow as before.
This is why household appliances are wired in parallel: each one gets the full supply voltage, and switching more of them on lowers the total resistance and raises the total current drawn, which is what fuses and circuit breakers guard against. Exam shortcut: n identical resistors R give R/n in parallel and nR in series.
Got this one? The Knot Scan finds the misconception you don't know you have, in 8 questions.