יסודות במדידות — 33.9001 · תורת החשמל לטכנאים

R_m = UI | δ = R_m − RR·100% | R₀ = √R_A·R_V

1.00 kΩ

1.0 Ω

100 kΩ

10.0 V

9.90 V

9.99 mA

990 Ω

1000 Ω

−9.9 Ω

−0.99 %

1000 Ω

+1.00 %

R₁ = R·R_VR + R_V R₂ = R + R_A

δ₁ = −0.01% | δ₂ = +100%

δ₁ = −50% | δ₂ = +0.01%

R = √R_A·R_V = √10 · 100000 = 1000 Ω

Δx = x_m − x | δ = Δxx·100% | x̄ = Σx_in | s² = Σ(x_i − x̄)²n − 1

100.0 V

+2.0 V

1.5 V

20

0

— V

100.0 V

— V

— %

— V

x̄ = 232 + 234 + 231 + 235 + 2335 = 233.0 V

Δx = 233.0 − 230 = +3.0 V

δ = 3.0230·100% = 1.30%

s ≈ 1.58 V | Δx = +3.0 V

Δx = k·x_max100 | δ = Δxx·100% = k·x_maxx | q = x_maxN | S = ΔαΔx

60.0 V

3½

300 V

±4.50 V

7.50 %

20 %

3.00 V

0.1 V

0.30 °/V

1.50 %

Δx = 1.5 · 300100 = 4.5 V

δ = 4.560·100% = 7.5%

Δx = 1.5 V δ = 1.560·100% = 2.5%

δ_min = k = 1.5%

U_out = A·(U_in + U_os) | CMRR = 20·log₁₀A_dA_cm dB | δ_tot = √δ_s² + δ_a² + δ_d²

60 °C

1.0 %

15

500 mV

90 dB

123.2 Ω

21.6 mV

2.16 V

1.58 mV

60.6 °C

+0.6 °C

0.1 °C

—

δ = √δ_s² + δ_a² + δ_d²

δ = √1.0² + 0.3² + 0.2² = √1.13 = 1.063%

δ = √1.0² + 0.1² + 0.2² = 1.025%

δ = √0.333² + 0.3² + 0.2² = 0.489%

P₁ = U_L·I_L·cos(30° − φ) | P₂ = U_L·I_L·cos(30° + φ) | P = P₁ + P₂ = √3·U_L·I_L·cosφ | tanφ = √3·P₁ − P₂P₁ + P₂ | I_L = k_CT·I_A

400 V

20.0 A

36.9°

7943 W

3143 W

11085 W

8314 var

13856 VA

0.800

1.00 A

231 V

I_A = 2020 = 1.0 A

φ = arccos(0.8) = 36.87° P₁ = 400 · 20 · cos(30° − 36.87°) = 7943 W P₂ = 400 · 20 · cos(30° + 36.87°) = 3143 W

P = 7943 + 3143 = 11086 W P = √3 · 400 · 20 · 0.8 = 11085 W

tanφ = √3·7943 − 314311086 = 0.750 φ = 36.87° → cosφ = 0.800

ΔX = X_read − X_true | δ = ΔXX_true·100 % | Δ_max = cl · X_range100

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