Physics · Current Electricity · NEET
Series always gives a BIGGER resistance than any single resistor because you simply add them: R_s = R1 + R2 + ... Parallel always gives a SMALLER resistance than even the smallest resistor, because adding more paths lets more current flow. Quick check: two 6 ohm resistors give 12 ohm in series but only 3 ohm in parallel.
In SERIES the CURRENT is the same through every resistor (one single path), while the voltage splits. In PARALLEL the VOLTAGE is the same across every resistor (all joined to the same two points), while the current splits. Memory line: Series = Same current; Parallel = same Potential (voltage).
Each parallel branch is an extra road for current. More roads mean the charges find it easier to flow, so the combined opposition drops. Even one branch already carries current; adding a second branch only adds more, so total resistance must fall below the smallest single branch. Mathematically, for two resistors R_p = R1 R2 / (R1 + R2), which is smaller than both.
If each resistor is R and there are n of them: series gives nR, parallel gives R/n. So R_series / R_parallel = nR / (R/n) = n squared. That is why NEET loves this trick: turning 10 equal resistors from series to parallel multiplies the current by n^2 = 100 (if the battery has negligible internal resistance).
Use the product-over-sum shortcut: R_p = (R1 x R2) / (R1 + R2). For 100 and 200 it is (100 x 200)/300 = 66.7 ohm. Special case: two EQUAL resistors R in parallel = R/2. This only works for exactly TWO resistors; for three or more, use 1/R_p = 1/R1 + 1/R2 + 1/R3.
The effective resistance of four identical wires in parallel is 0.25 ohm. Their effective resistance in series is:
10 resistors (R each) are connected in series with a battery of emf E and negligible internal resistance; then they are connected in parallel. The current increases n times. The value of n is:
A wire of resistance 100 ohm is divided into 10 equal parts. The first 5 parts are connected in series, the next 5 in parallel; the two combinations are then joined in series. The resistance of the final combination is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Series: resistors add (R_s = R1 + R2 + ...), same current, bigger total. Parallel: reciprocals add (1/R_p = 1/R1 + 1/R2 + ...), same voltage, smaller total.
Series gives higher resistance (it adds up). Parallel gives lower resistance, always less than the smallest resistor in the group.
Product over sum: R_p = (R1 x R2) / (R1 + R2). Two equal resistors R in parallel give exactly R/2.
Series = nR, parallel = R/n, so the ratio R_series : R_parallel = n^2 : 1. The current therefore rises by a factor of n^2 for the same battery (negligible internal resistance).
In SERIES the same current flows through every resistor because there is only one path. In parallel the current splits between branches.
