Resistors and capacitors
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A resistor limits current; a capacitor stores charge. Read a real resistor's colour bands (brown, black, red, gold: 1 kΩ ±5 %), look inside a capacitor at its two plates, and learn Q = C × V and the farad. Then close a switch and watch a 1000 µF capacitor charge through 1 kΩ along the RC curve: 63 % after one time constant τ = R × C, over 99 % after five. Finish with what capacitors are used for.
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01A resistor has the bands brown, black, red, gold. What is its value?
Brown = 1 and black = 0 give the digits 10. Red as the third band means multiply by 100, so 10 × 100 = 1,000 Ω (1 kΩ). Gold is the tolerance: ±5 %, so 950 to 1,050 Ω.
02A 1000 µF capacitor is charged to 5 V. How much charge does it hold?
Q = C × V = 0.001 F × 5 V = 0.005 C, which is 5 millicoulombs. 1000 µF is 1000 millionths of a farad, that is 0.001 F.
03A 1 kΩ resistor charges a 1000 µF capacitor. What is the time constant τ?
τ = R × C = 1,000 Ω × 0.001 F = 1 second.
04Roughly how far has a capacitor charged after one time constant, and after five?
After 1 τ the voltage is about 63 % (63.2 %) of the way to the battery voltage; after 5 τ it is above 99 % (99.3 %). The curve keeps slowing down because the capacitor's own voltage pushes back.
05Why is a small capacitor placed right next to a chip's power pins?
A decoupling capacitor (often 0.1 µF) holds a little charge right where the chip needs it, so sudden bursts of current do not make the supply voltage dip.
المسرد
- Resistor
- A part that makes it harder for current to flow. Its resistance is measured in ohms (Ω).
- Ohm (Ω)
- The unit of resistance. 1 kΩ (kilo-ohm) is 1,000 ohms.
- Colour code
- Coloured bands on a resistor that give its value: two digits, a multiplier and a tolerance.
- Tolerance
- How far the real value may be from the printed one. A gold band means within ±5 %.
- Capacitor
- Two metal plates with a thin insulator between them. It stores electric charge.
- Farad (F)
- The unit of capacitance: how much charge a capacitor stores per volt (Q = C × V). Real parts are measured in µF (millionths) and nF (billionths).
- Time constant (τ)
- τ = R × C. After one τ a charging capacitor reaches about 63 % of the supply voltage; after five, over 99 %.
- Decoupling capacitor
- A small capacitor placed right next to a chip's power pins, as a local reserve of charge.
الملاحظات والمصادر
- The board is a teaching model: the 9 V battery is ideal (no internal resistance) and the lamp is treated as an ideal meter that draws no current. 1 kΩ and 1000 µF are picked so that τ = R × C = 1 s.
- The colour code is standardised in IEC 60062: two digit bands, a multiplier band and a tolerance band (gold ±5 %, silver ±10 %, brown ±1 %). The tolerance band usually sits a little apart from the others: start reading from the other end.
- Charging through a resistor: V(t) = V_bat (1 − e^(−t/RC)) and I(t) = (V_bat / R) e^(−t/RC) (OpenStax University Physics Volume 2, section 10.5). After 1 τ the voltage is 63.2 % of the way there, after 5 τ 99.3 %.
- Current is drawn in the conventional direction (from + to −); the electrons in the wires move the other way.
- Decoupling capacitors, typically 0.1 µF, go as close as possible to a chip's power pins (Analog Devices tutorial MT-101).
- OpenStax, University Physics Volume 2: 10.5 RC Circuits
- OpenStax, University Physics Volume 2: 8.1 Capacitors and Capacitance
- OpenStax, University Physics Volume 2: 9.3 Resistivity and Resistance
- Digi-Key: Resistor colour code (IEC 60062)
- MIT OCW 6.002: Circuits and Electronics
- NIST: Metric (SI) prefixes
- Analog Devices MT-101: Decoupling Techniques
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