3.1 Elektr Asoslari — Masalalar

Jami: 30 ta | Yechim bilan: ✅

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Asosiy Masalalar (1-12)

Masala 1 ⭐⭐

12 V batareya 4 Ω qarshilikka ulangan. Tok va quvvat?

Yechim

$I = \frac{V}{R} = \frac{12}{4} = 3$ A

$P = VI = 12 \times 3 = 36$ W

Yoki: $P = I^2R = 9 \times 4 = 36$ W

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Masala 2 ⭐⭐

LED: 20 mA tok, 2V kuchlanish tushishi. 5V manbadan qaysi rezistor kerak?

Yechim

Rezistordagi kuchlanish: $V_R = 5 - 2 = 3$ V

$R = \frac{V_R}{I} = \frac{3}{0.02} = 150$ Ω

Quvvat: $P = V_R \times I = 3 \times 0.02 = 0.06$ W = 60 mW

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Masala 3 ⭐⭐

Ketma-ket: 100Ω, 200Ω, 300Ω. Ekvivalent qarshilik?

Yechim

$R_{eq} = 100 + 200 + 300 = 600$ Ω

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Masala 4 ⭐⭐

Parallel: 100Ω va 100Ω. Ekvivalent?

Yechim

$R_{eq} = \frac{R_1 \times R_2}{R_1 + R_2} = \frac{100 \times 100}{200} = 50$ Ω

Qoida: n ta teng R parallel = R/n

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Masala 5 ⭐⭐

Kuchlanish bo'lgich: R₁ = 10kΩ, R₂ = 5kΩ, Vin = 12V. Vout?

Yechim

$V_{out} = V_{in} \times \frac{R_2}{R_1 + R_2} = 12 \times \frac{5}{15} = 4$ V

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Masala 6 ⭐⭐

RC zanjir: R = 10kΩ, C = 100μF. Vaqt konstantasi?

Yechim

$\tau = RC = 10000 \times 100 \times 10^{-6} = 1$ s

5τ ≈ 5 s (to'liq zaryadlanish)

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Masala 7 ⭐⭐

Motor 12V, 2A tok oladi. Quvvat va 1 soatda energiya sarfi?

Yechim

$P = VI = 12 \times 2 = 24$ W

$E = P \times t = 24 \times 3600 = 86400$ J = 24 Wh

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Masala 8 ⭐⭐

3.7V LiPo, 2000mAh. Energiya (Wh) va (J)?

Yechim

$E = V \times Q = 3.7 \times 2 = 7.4$ Wh

$E = 7.4 \times 3600 = 26640$ J ≈ 26.6 kJ

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Masala 9 ⭐⭐

Kondensator: C = 1000μF, V = 5V. Saqlangan energiya?

Yechim

$E = \frac{1}{2}CV^2 = \frac{1}{2}(0.001)(25) = 0.0125$ J = 12.5 mJ

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Masala 10 ⭐⭐

Servo motor: 5V, standby 10mA, max 500mA. Quvvat diapazoni?

Yechim

Min: $P_{min} = 5 \times 0.01 = 0.05$ W = 50 mW

Max: $P_{max} = 5 \times 0.5 = 2.5$ W

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Masala 11 ⭐⭐

Pull-up rezistor: 10kΩ, 3.3V. Tugma bosilganda tok?

Yechim

Tugma bosilganda pin GND ga ulanadi:

$I = \frac{V}{R} = \frac{3.3}{10000} = 0.33$ mA

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Masala 12 ⭐⭐

ADC: 10-bit, Vref = 5V. Bit boshiga kuchlanish (LSB)?

Yechim

$LSB = \frac{V_{ref}}{2^{10}} = \frac{5}{1024} = 4.88$ mV

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O'rtacha Masalalar (13-22)

Masala 13 ⭐⭐⭐

Murakkab zanjir: (R1 || R2) ketma-ket R3. R1=R2=100Ω, R3=50Ω. Ekvivalent?

Yechim

$R_{12} = \frac{100 \times 100}{200} = 50$ Ω

$R_{eq} = R_{12} + R_3 = 50 + 50 = 100$ Ω

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Masala 14 ⭐⭐⭐

RC filtr: R = 1kΩ, C = 0.1μF. Cutoff chastotasi?

Yechim

$f_c = \frac{1}{2\pi RC} = \frac{1}{2\pi \times 1000 \times 0.0000001} = 1592$ Hz ≈ 1.6 kHz

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Masala 15 ⭐⭐⭐

H-bridge: 4 ta MOSFET, Rds = 0.01Ω har biri. Motor 5A tok oladi. MOSFETlarda quvvat yo'qotish?

Yechim

Har bir vaqtda 2 ta MOSFET yoqiq:

$P_{total} = 2 \times I^2 R_{ds} = 2 \times 25 \times 0.01 = 0.5$ W

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Masala 16 ⭐⭐⭐

Buck converter: Vin = 12V, Vout = 5V, I = 2A, η = 90%. Kirish toki?

Yechim

Chiqish quvvati: $P_{out} = 5 \times 2 = 10$ W

Kirish quvvati: $P_{in} = \frac{P_{out}}{\eta} = \frac{10}{0.9} = 11.1$ W

Kirish toki: $I_{in} = \frac{P_{in}}{V_{in}} = \frac{11.1}{12} = 0.93$ A

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Masala 17 ⭐⭐⭐

Batareya: 11.1V (3S LiPo), 5000mAh, dron 15A o'rtacha tok. Uchish vaqti?

Yechim

$t = \frac{Q}{I} = \frac{5000}{15000} = 0.333$ h = 20 min

(Real: 80% foydalanish → 16 min)

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Masala 18 ⭐⭐⭐

Wheatstone bridge: R1=R2=R3=1kΩ, Rx=?. Vg=0 bo'lganda Rx?

Yechim

Muvozanat sharti: $\frac{R_1}{R_2} = \frac{R_3}{R_x}$

$R_x = \frac{R_2 \times R_3}{R_1} = \frac{1000 \times 1000}{1000} = 1000$ Ω = 1kΩ

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Masala 19 ⭐⭐⭐

Sensor output: 0-3.3V. ADC Vref = 5V. Maximum ADC qiymati?

Yechim

10-bit ADC: $ADC_{max} = \frac{3.3}{5} \times 1023 = 675$

Yoki 12-bit: $ADC_{max} = \frac{3.3}{5} \times 4095 = 2703$

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Masala 20 ⭐⭐⭐

PWM motor control: 12V, 50% duty cycle. O'rtacha kuchlanish?

Yechim

$V_{avg} = V_{in} \times D = 12 \times 0.5 = 6$ V

(Bu idealized — induktiv yuk filtrlanadi)

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Masala 21 ⭐⭐⭐

Termorezistor (NTC): 25°C da 10kΩ, β=3950. 50°C da qarshilik?

Yechim

$R(T) = R_0 \exp\left[\beta\left(\frac{1}{T} - \frac{1}{T_0}\right)\right]$

$T_0 = 298K$, $T = 323K$

$R = 10000 \exp\left[3950\left(\frac{1}{323} - \frac{1}{298}\right)\right]$

$= 10000 \exp[3950 \times (-0.000259)]$

$= 10000 \exp(-1.023) = 10000 \times 0.36 = 3600$ Ω

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Masala 22 ⭐⭐⭐

Regenerative braking: Motor 100W teskari energiya qaytarmoqda. 12V batareya. Tok?

Yechim

$I = \frac{P}{V} = \frac{100}{12} = 8.33$ A

(Charging current — batareya signifikatsiyasi tekshirilishi kerak)

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Murakkab Masalalar (23-30)

Masala 23 ⭐⭐⭐⭐

AC-DC rectifier: 12V AC (RMS). DC output (full-bridge, no smoothing)?

Yechim

Peak AC: $V_{peak} = 12\sqrt{2} = 16.97$ V

Full-bridge rectifier average (no capacitor): $V_{DC} = \frac{2V_{peak}}{\pi} = \frac{2 \times 16.97}{3.14} = 10.8$ V

With smoothing capacitor: ≈ 15-16V (under light load)

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Masala 24 ⭐⭐⭐⭐

Op-amp non-inverting: Vin = 0.5V, R1 = 10kΩ, Rf = 90kΩ. Vout?

Yechim

$A_v = 1 + \frac{R_f}{R_1} = 1 + \frac{90}{10} = 10$

$V_{out} = A_v \times V_{in} = 10 \times 0.5 = 5$ V

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Masala 25 ⭐⭐⭐⭐

LC rezonans: L = 1mH, C = 10nF. Rezonans chastotasi?

Yechim

$f_0 = \frac{1}{2\pi\sqrt{LC}} = \frac{1}{2\pi\sqrt{10^{-3} \times 10^{-8}}}$

$= \frac{1}{2\pi \times 10^{-5.5}} = \frac{1}{2\pi \times 3.16 \times 10^{-6}} = 50.3$ kHz

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Masala 26 ⭐⭐⭐⭐

ESC (Electronic Speed Controller): 3S LiPo (11.1V), motor Kv=1000 rpm/V, no-load. Max RPM?

Yechim

$RPM = K_v \times V = 1000 \times 11.1 = 11100$ RPM

(Real: ~10-15% kamroq yuklangan holatda)

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Masala 27 ⭐⭐⭐⭐

Zener voltage regulator: Vin = 15V, Vz = 5V, Iz_min = 5mA, Rload = 100Ω. Series rezistor?

Yechim

Load tok: $I_L = \frac{5}{100} = 50$ mA

Zener orqali: $I_z = I_z + I_L$ (kamida)

Series R: $R_s = \frac{V_{in} - V_z}{I_z + I_L} = \frac{15 - 5}{0.005 + 0.05} = \frac{10}{0.055} = 182$ Ω

Quvvat: $P_{Rs} = I^2 R = 0.055^2 \times 182 = 0.55$ W → 1W rezistor kerak

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Masala 28 ⭐⭐⭐⭐

I2C pull-up: 3.3V, 4.7kΩ. Bus capacitance 100pF. Rise time?

Yechim

Rise time (10% to 90%): $t_r = 2.2 \times R \times C = 2.2 \times 4700 \times 100 \times 10^{-12}$

$= 1.03$ μs

I2C standard: max 1μs → bu chegarada

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Masala 29 ⭐⭐⭐⭐

BLDC motor: 14 poles, 12 slots, 1000 RPM. Electrical frequency?

Yechim

Pole pairs: $p = 14/2 = 7$

$f_e = \frac{RPM \times p}{60} = \frac{1000 \times 7}{60} = 116.7$ Hz

Commutation frequency: $f_c = 6 \times f_e = 700$ Hz (6-step)

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Masala 30 ⭐⭐⭐⭐

Decoupling capacitor: 100nF, ESR = 0.05Ω, ESL = 1nH. Impedance 10 MHz da?

Yechim

$X_C = \frac{1}{2\pi f C} = \frac{1}{2\pi \times 10^7 \times 10^{-7}} = 0.159$ Ω

$X_L = 2\pi f L = 2\pi \times 10^7 \times 10^{-9} = 0.063$ Ω

$Z = \sqrt{ESR^2 + (X_L - X_C)^2} = \sqrt{0.0025 + 0.0092} = 0.108$ Ω

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✅ Tekshirish Ro'yxati

• 1-12: Asosiy zanjir masalalari
• 13-22: RC, filtr, ADC
• 23-30: Murakkab masalalar

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