מעגלי זרם ישר
✦ בנוי על ידי פהד גאנם ✦
العربية
☀ מצב בהיר
3.1
▾
✕
I =
Q
t
| Q = I·t | v_d =
I
n·e·A
| N =
Q
e
2.00 A
1.0 mm²
5.0×10²⁸ m⁻³
0.00
0.00
0.00
0.0000
0
—
Q = I·t = 0.25 · 40 = 10 C
N =
Q
e
=
10
1.6·10⁻¹⁹
= 6.25·10¹⁹
N = 6.25·10¹⁹
3.2
▾
✕
V = I·R | I =
V
R
| R =
V
I
| P = V·I = I²R =
V²
R
0.0 V
24 Ω
0.0
0.00
0.000
24.0
0.00
0.00
R =
V
I
=
12
0.50
= 24 Ω
P = V·I = 12 · 0.50 = 6 W
P = I²R = 0.25 · 24 = 6 W
P =
V²
R
=
144
24
= 6 W
I =
V
R
=
24
24
= 1.0 A
P = V·I = 24 · 1.0 = 24 W
3.3
▾
✕
R =
ρ·L
A
| I =
V
R + R
L
| V
out
= V ·
R
1
R
1
+ R
2
20.0 m
0.80 mm²
50 %
0
0
0
0
0
0
0
0
0
0
0
0
r =
d
2
=
1.0 mm
2
= 0.50 mm = 0.50·10⁻³ m
A = π·r² = π·(0.50·10⁻³)² = 7.85·10⁻⁷ m² = 0.785 mm²
R =
ρ·L
A
=
1.68·10⁻⁸ · 20
7.85·10⁻⁷
= 0.428 Ω
A′ = π·(
r
2
)² =
A
4
= 1.96·10⁻⁷ m²
R′ =
ρ·L
A′
=
1.68·10⁻⁸ · 20
1.96·10⁻⁷
= 4R = 1.71 Ω
3.4
▾
✕
I =
ε
R + r
| V = ε − I·r = I·R | P
r
= I²·r
12.0 V
0.50 Ω
5.5 Ω
0.00
0.00
0.00
0.00
0.00
0.00 W
R + r = 5.5 + 0.50 = 6.0 Ω
I =
ε
R + r
=
12
6.0
= 2.0 A
V = ε − I·r = 12 − 2.0 · 0.50 = 11.0 V
V = I·R = 2.0 · 5.5 = 11.0 V
P_r = I²·r = 2.0² · 0.50 = 2.0 W
3.5
▾
✕
τ = R·C | Vc = V₀·(1 − e
−
t
τ
) | I =
V₀
R
·e
−
t
τ
| Q = C·Vc
12 V
10 kΩ
100 µF
0.00
1.00
0.00
0.000
0.000
0.000
R = 10 kΩ = 1.0·10⁴ Ω
C = 100 µF = 1.0·10⁻⁴ F
τ = R·C = 1.0·10⁴ · 1.0·10⁻⁴ = 1.0 s
I₀ =
V₀
R
=
12
1.0·10⁴
= 1.2·10⁻³ A = 1.2 mA
Vc = V₀·(1 − e⁻¹) = 12 · (1 − 0.368) = 12 · 0.632
3.6
▾
✕
P = V·I = I²R | η =
P_out
P_in
| E = P·t
500 V
5000 W
5.0 Ω
2000 W
3.0 h
0.60 ₪
0
0
0
0
0
0
0
0
E = P·t = 2.0 kW · 3.0 h = 6.0 kWh
P_in = V·I = 12 · 5.0 = 60 W
W = mgh = 4.0 · 9.8 · 1.5 = 58.8 J
P_out =
W
t
=
58.8
3.0
= 19.6 W
η =
P_out
P_in
=
19.6
60
= 0.327
3.7
▾
✕
R = R1 + R2 + R3 |
1
R
=
1
R1
+
1
R2
+
1
R3
| ΣI = 0 | ΣU = 0
12.0 V
9.0 V
6.0 Ω
6.0 Ω
3.0 Ω
0
0
0
I1
0
I2
0
I3
0
U1
0
U2
0
U3
0
0
0
0
0
R23 =
R2 · R3
R2 + R3
R23 =
6.0 · 3.0
6.0 + 3.0
=
18
9
= 2.0 Ω
R = R1 + R23 = 6.0 + 2.0 = 8.0 Ω
I =
V
R
=
12
8.0
= 1.5 A
U23 = 1.5 · 2.0 = 3.0 V
I2 =
U23
R2
=
3.0
6.0
= 0.50 A
I3 =
U23
R3
=
3.0
3.0
= 1.0 A
0.50 + 1.0 = 1.5 A
3.8
▾
✕
V = E ·
R₁∥Rv
R₁∥Rv + R₂
| I =
E
R₁ + R₂ + Ra
12.0 V
10 kΩ
10 kΩ
100 kΩ
10 Ω
0
0
0
0
0
0
V₁ = E ·
R₁
R₁ + R₂
= 10 ·
100k
100k + 100k
= 5.00 V
Rp =
R₁ · Rv
R₁ + Rv
=
100k · 100k
100k + 100k
= 50 kΩ
Rtot = Rp + R₂ = 50k + 100k = 150 kΩ
I =
E
Rtot
=
10
150k
= 66.7 µA
V = I · Rp = 66.7 µA · 50k = 3.33 V
δ =
V − V₁
V₁
=
3.33 − 5.00
5.00
= −33.3 %
→
🏠
♿