3.1 Elektr Asoslari — Nazariya

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Kirish

Elektronika — robotika, dronlar va raketalarning "asab tizimi". Bu bo'limda elektr zanjirlarining asoslarini o'rganamiz.

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1. Asosiy Kattaliklar

Kuchlanish (Voltage)

Kuchlanish (V) — elektr potensiallar farqi, elektronlarni harakatga keltiruvchi "bosim".

$$V = \frac{W}{Q}$$

• $V$ — kuchlanish (Volt)
• $W$ — energiya (Joule)
• $Q$ — zaryad (Coulomb)

O'xshatish

Kuchlanish = suv quvuridagi bosim farqi

Tok (Current)

Tok (I) — zaryadning oqimi, sekundiga o'tgan zaryad miqdori.

$$I = \frac{Q}{t} = \frac{dQ}{dt}$$

• $I$ — tok (Amper)
• 1 A = 1 Kulon/sekund

Qarshilik (Resistance)

Qarshilik (R) — materialning tokka qarshiligi.

$$R = \rho \frac{L}{A}$$

• $\rho$ — solishtirma qarshilik (Ω·m)
• $L$ — uzunlik
• $A$ — kesim yuza

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2. Ohm Qonuni

Asosiy munosabat:

$$V = I \cdot R$$

Yoki:

$$I = \frac{V}{R}, \quad R = \frac{V}{I}$$

Quvvat

$$P = V \cdot I = I^2 R = \frac{V^2}{R}$$

• $P$ — quvvat (Watt)

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3. Kirchhoff Qonunlari

Tok Qonuni (KCL)

Tugunga kirgan toklar yig'indisi = chiqqan toklar yig'indisi.

$$\sum I_{in} = \sum I_{out}$$

Yoki: $\sum I = 0$ (kirganlar +, chiqqanlar -)

Kuchlanish Qonuni (KVL)

Yopiq konturda kuchlanishlar yig'indisi = 0.

$$\sum V = 0$$

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4. Ketma-ket va Parallel Ulanish

Qarshiliklar

Ketma-ket:

$$R_{eq} = R_1 + R_2 + R_3 + \ldots$$

Parallel:

$$\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \ldots$$

Ikki qarshilik uchun:

$$R_{eq} = \frac{R_1 \cdot R_2}{R_1 + R_2}$$

Kondensatorlar

Ketma-ket:

$$\frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2}$$

Parallel:

$$C_{eq} = C_1 + C_2$$

Induktorlar

Qarshiliklar kabi (ketma-ketda qo'shiladi).

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5. Kondensator va Induktor

Kondensator

Energiya saqlovchi (elektr maydonida):

$$Q = C \cdot V$$ $$i = C \frac{dV}{dt}$$

Energiya:

$$E = \frac{1}{2}CV^2$$

Induktor

Energiya saqlovchi (magnit maydonida):

$$V = L \frac{di}{dt}$$

Energiya:

$$E = \frac{1}{2}LI^2$$

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6. RC va RL Zanjirlar

RC Zanjir

Zaryadlanish:

$$V_C(t) = V_s(1 - e^{-t/\tau})$$

Razryadlanish:

$$V_C(t) = V_0 e^{-t/\tau}$$

Vaqt konstantasi:

$$\tau = R \cdot C$$

RL Zanjir

$$I(t) = I_{max}(1 - e^{-t/\tau})$$ $$\tau = \frac{L}{R}$$

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7. Sensorlar uchun Kuchlanish Bo'lgich

$$V_{out} = V_{in} \cdot \frac{R_2}{R_1 + R_2}$$

Qo'llanilishi

• Batareya kuchlanishini o'lchash (ADC uchun)
• Sensor signallarini moslashtirish
• Reference voltage yaratish

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8. Robotikada Qo'llanilish

Motor Driver

• H-bridge: yo'nalish va tezlik
• PWM: analog kuchlanish modulyatsiyasi

Sensor Interfacing

• Analog sensorlar → ADC
• Pull-up/pull-down rezistorlar
• RC filtrlar

Power Distribution

• Voltage regulator
• Batareya monitoring
• Quvvat boshqarish

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Xulosa

Tushuncha	Formula	Birlik
Ohm qonuni	$V = IR$	V, A, Ω
Quvvat	$P = VI$	W
Ketma-ket R	$R = R_1 + R_2$	Ω
Parallel R	$R = \frac{R_1R_2}{R_1+R_2}$	Ω
RC vaqt	$\tau = RC$	s
Kondensator E	$E = \frac{1}{2}CV^2$	J

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