Multimeter Technique & Resistor Networks

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.title[
# Multimeter Technique & Resistor Networks
]
.subtitle[
## Programmable Electronics — Unit 1
]
.date[
### Class 4
]

---

# Learning Targets

.lt-box[
- Correctly measure voltage (multimeter in parallel) and current (multimeter in series), and explain why each requires that configuration.
- Predict, then measure, total resistance, current, and voltage in series and parallel resistor networks.
- Calculate the power dissipated by a resistor (`$P = IV$`) and explain why resistors have a power rating.
- Reconcile differences between predicted and measured values, identifying likely sources of error.
]

.eu-label[Essential Understanding:] Measuring a circuit changes *how* you have to connect the meter. Get that wrong and you get nonsense — or a blown fuse. Series and parallel networks behave predictably, but only if you check the prediction against reality.

---

# Agenda

.agenda-box[
1. Recap: where the water-tank analogy breaks down
2. Multimeter technique: measuring voltage vs. current
3. Series resistor networks
4. Parallel resistor networks
5. Power and the wattage rating
6. **Build (25–30 min):** Predict, Build, Measure, Reconcile
7. Homework
]

---

# Recap: where the analogy breaks down

The water-tank picture from Class 2 was great for **one** tank, **one** hose, **one** path.

Today every circuit has *more than one path* — and "more water" doesn't tell you how it splits between two hoses of different widths.

That's exactly what **series** and **parallel** describe: how current behaves when there's more than one component, or more than one path, to share.

---

# Two things a multimeter measures

A multimeter can measure voltage, current, and resistance — but **how you connect it changes based on what you're measuring**.

- **Voltage** is measured *across* two points — touch the probes to both ends of a component, without disconnecting anything.
- **Current** is measured *through* a path — you have to break the circuit and let the meter become part of it.

---

# Measuring voltage (parallel)

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.pull-right.w40[
- The meter's leads touch the two ends of the resistor.
- The loop stays **closed** the whole time — the circuit doesn't know the meter is there.
- This is why you can measure voltage on a live circuit without disturbing it.
]

---

# Measuring current (series)

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.pull-right.w40[
- The wire has to be **cut**, and the meter is inserted into the gap.
- The meter *becomes* part of the path — every electron has to pass through it.
- This is why swapping voltage and current probe positions is a classic mistake: putting an ammeter *across* a component instead of *in* the path creates a near-short circuit through the meter.
]

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# Quick check

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Where would you put the meter — and in what mode — to measure:

1. The voltage across R2 only?
2. The current flowing through R1?

Talk it over with your partner before we move on.

---

# Series resistors

.pull-left.w50[
- One path. The same current flows through every resistor.
- Resistances **add**:

`$$R_{total} = R_1 + R_2 + \dots + R_n$$`

- Voltage divides across each resistor, proportional to its share of the total resistance.
]
.pull-right.w45[
**Quick exercise:** 220 Ω and 330 Ω in series, off a 6 V supply.

- `$R_{total} = ?$`
- `$I = ?$` (same through both)
- `$V$` across each resistor?

Show your work in your notebook.
]

---

# Parallel resistors

.pull-left.w50[
- Multiple paths. The same voltage appears across every branch.
- Resistances combine — total resistance is always **less** than the smallest branch:

`$$\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots + \frac{1}{R_n}$$`

- Current divides between branches — more current takes the path of *less* resistance.
]
.pull-right.w45[
**Quick exercise:** 220 Ω and 330 Ω in parallel.

- `$R_{total} = ?$`
- Which resistor carries more current, if both see the same voltage?

Show your work in your notebook.
]

---

# Power and the wattage rating

Every resistor has a maximum power it can safely dissipate as heat — printed on the datasheet, not on the part.

`$$P = IV$$`

**Check it against your own circuit:** your Class 3 LED driver ran about 27.27 mA through a 220 Ω resistor at 6 V.

`$$P = I \times V = 0.02727\,\text{A} \times 6\,\text{V} \approx 0.164\,\text{W}$$`

Most kit resistors are rated for **¼ W (0.25 W)** — this one runs well within its rating. Exceed the rating and a resistor overheats, discolors, or smokes.

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# Build (25–30 min): Predict, Build, Measure, Reconcile

Choose two different resistors from your kit and work through both configurations.

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# Build instructions

With your partner, using your breadboard, 6 V battery pack, and multimeter:

1. Sketch a **series** circuit in your notebook: your two resistors, off the 6 V supply.
2. **Predict** total resistance, current, and the voltage across each resistor. Show your work.
3. **Build** it. **Measure** the actual voltage across each resistor and the actual current through the loop — remember, break the circuit to insert the ammeter.
4. Rewire the same two resistors in **parallel**. Predict, build, and measure again.
5. For each configuration, calculate the power dissipated by each resistor. Confirm you're within its rating.
6. **Reconcile:** wherever prediction and measurement disagree, write your best explanation why.