108年 - 108 國立臺北大學_日間學士班轉學生招生考試試題_電機工程學系日間學士班2年級：普通物理#147491

(1) Find the parameters \( k \), \( \omega \), and \( \varphi \) (9%)

(2) Find the speed of the wave \( (3\%) \)

(3) What is the transverse velocity of the particle at \( x = 0 \) when \( t = 5.0s \)? (4%)

2. Fig.2 shows a circuit section of four air-filled capacitors that is connected to a larger circuit. The graph below the section shows the electric potential V(x) as a function of position x along the lower part of the section, through capacitor 4. Similarly, the graph above the section shows the electric potential V(x) as a function of position x along the upper part of the section, through capacitors 1, 2, and 3. Capacitor 3 has a capacitance of 0.8 μF. What are the capacitances of (a) capacitor 1 (4%) and (b) capacitor 2 ? (4%)

3. Find the current i in Fig. 3. (5%)

4. Find the current \( I \) in Fig. 4. (5%)

5. Find the current $I_1$ in Fig. 5. (5%)

6. Find the current \( I_1 \) and \( I_2 \) in Fig. 6. (10%)

7. Find the current \( I_1 \) pass through the \( 8\Omega \) resistor and the short-circuit current \( I_2 \) in Fig. 7. (15%, 5% for \( I_1 \) and 10% for \( I_2 \))

8. The wire is 10m long with 5A current passing through. The directions of the magnetic fields are shown in Fig. 8a and 8b. Their magnetic flux densities are both $1Wb/m^2$. Find the two magnetic forces on the current-carrying wires in Fig. 8a and 8b. (10%)

9. In Fig. 9, ε=100V, R1=10Ω, R2=20Ω, R3=30Ω, and L=2H. Immediately after switch S is closed, what are (a) i₁ and (b) i₂? A long time later, what are (c) i₁ and (d) i₂? The switch S is then reopened. Just then, what are (e) i₁ and (f) i₂? A long time later, what are (g) i₁ and (h) i₂? (16%)

10. For the magnetic circuit of Fig. 10, the current \( i \) flows through the coil of \( N \) turns. The mean core length is \( \ell_c \), and the air gap length is \( \ell_g \). Assume no magnetic leakage. The flux crossing the cross-sectional area \( A \). The relative permeability of core is \( \mu_r \). The permeability of air is \( \mu_0 \). Find the flux in the air gap. (10%)