Practical case: Equivalent resistance in series and parallel

Materials

• 1 × DC power supply (5 V)
• 1 × Breadboard
• 4 × Resistors: R1 = 1 kΩ, R2 = 2.2 kΩ, R3 = 1 kΩ, R4 = 2.2 kΩ (1/4 W)
• 2 × Digital multimeters (or 1 reused for both branches)
• 8 × Jumper wires (male–male)
• 2 × Extra jumpers for inserting/removing ammeters if reusing 1 DMM

Wiring guide

• Build a common power rail: connect the DC supply +5 V to the top rail (+V) and the supply ground to the bottom rail (GND).
• Left branch (series network):
• From +V, insert the ammeter in current mode labeled A_SER in series.
• After A_SER, place R1 (1 kΩ) vertically, then connect its bottom to the top of R2 (2.2 kΩ) vertically.
• Connect the bottom of R2 to the GND rail.
• Add the voltage measurement dots: V_SER+ at the node between A_SER and R1; V_SER- at the node between R2 and GND.
• Right branch (parallel network):
• From +V, insert the ammeter in current mode labeled A_PAR in series.
• From the node after A_PAR, split to two vertical resistors in parallel: R3 (1 kΩ) and R4 (2.2 kΩ).
• Join the bottoms of R3 and R4 and connect that node to GND.
• Add the voltage measurement dots: V_PAR+ at the node between A_PAR and the split; V_PAR- at the common bottom node above GND.
• Abbreviations used:
• A_SER: ammeter measuring current through the series branch.
• A_PAR: ammeter measuring current through the parallel branch.
• V_SER+, V_SER-: red/black probe points to measure voltage across the series branch.
• V_PAR+, V_PAR-: red/black probe points to measure voltage across the parallel branch.
• Set one DMM to current mode (A or mA range) for A_SER and the other to current mode for A_PAR. If using a single DMM, measure one branch at a time by inserting it in series at the labeled locations.

Schematic

      Circuito 1: Serie (R1 + R2)                         Circuito 2: Paralelo (R3 || R4)

      +5 V ────────────────┐                              +5 V ────────────────┬───────────────┐
                            │─●VT1+                                             │               │
                            │                                                  ┌┴┐             ┌┴┐
                          ┌┴┐   R1 = 1 kΩ (M: R1)                              │ │  R3 = 1 kΩ  │ │  R4 = 1 kΩ
                          │ │                                                  │ │  (M: R3)    │ │  (M: R4)
                          │ │                                                  └┬┘             └┬┘
                          └┬┘                                                    │               │
                            │                                                  ──┴───────┬───────┴──
                          ┌┴┐   R2 = 2.2 kΩ (M: R2)                              │       │
                          │ │                                                    │       │
                          │ │                                                    │       │
                          └┬┘                                                    │       │
                            │─●VR1+                                              │       │
                          ┌┴┐   RS1 = 10 Ω (M: RS1, sensor)                    ┌┴┐
                          │ │                                                  │ │  RS2 = 10 Ω (M: RS2, sensor)
                          │ │                                                  │ │
                          └┬┘                                                  └┬┘
                            │─●VR1−                                              │─●VR2+ 
                            │                                                    │
      GND ──────────────────┘─●VT1−                       GND ──────────────────┘─●VT2−   ●VR2−

Measurements and tests

• Before powering:

  • Verify the ammeters are in current mode and wired in series (A_SER in the left branch, A_PAR in the right branch).
  • Confirm resistors match the marked values and there are no shorts between +V and GND.

• Record voltages:

  • Using the voltmeter mode, measure V_SER across ● V_SER+ (red) and ● V_SER- (black).
  • Measure V_PAR across ● V_PAR+ (red) and ● V_PAR- (black).
  • Expect both near 5.00 V if meters and wiring are correct.

• Record currents:

  • Read I_SER on A_SER (current through the series branch).
  • Read I_PAR on A_PAR (total current through the parallel branch).

• Calculate equivalent resistances:

  • R_EQ_SER = V_SER / I_SER. Theoretical: R1 + R2 = 1.0 kΩ + 2.2 kΩ = 3.2 kΩ.
  • R_EQ_PAR = V_PAR / I_PAR. Theoretical: (R3 × R4) / (R3 + R4) = (1.0 kΩ × 2.2 kΩ) / (1.0 kΩ + 2.2 kΩ) ≈ 687 Ω.

• Optional cross-check (power OFF first):

  • Remove power, take out the ammeter jumpers, and measure resistance directly across V_SER+/V_SER- and V_PAR+/V_PAR- with the ohmmeter. Values should match the computed equivalents within tolerance.

Common mistakes

• Ammeter in parallel: placing the ammeter across a node to GND will short the supply. Always insert it in series at A_SER or A_PAR.
• Measuring resistance with power applied: always power off before using the ohmmeter function.
• Miswiring the parallel branch: ensure R3 and R4 share the same top node and the same bottom node.
• Wrong DMM jack selection: use the correct current jack (often separate mA/μA or A) and range.

Safety notes

• With 5 V and ≥1 kΩ resistors, currents stay below 5 mA per path; power in each resistor is well under 0.1 W. Still, avoid touching exposed conductors and double-check there are no shorts before powering.
• Do not exceed the ammeter’s current rating and fuse limits.

Improvements

• Try different resistor pairs (e.g., 1 kΩ + 1 kΩ) and verify how R_EQ changes for series vs parallel.
• Add a third resistor to the series branch or a third leg in the parallel branch and predict/measure the new equivalent.
• Replace the DC supply with another voltage (e.g., 9 V) and verify R_EQ stays the same while currents scale with V.

More Practical Cases on Prometeo.blog

Carlos Núñez Zorrilla

Electronics & Computer Engineer

Telecommunications Electronics Engineer and Computer Engineer (official degrees in Spain).

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