SCE FE Electrical Complete Review Guide 2026–2027

4. In DC steady state an inductor acts as a short circuit and a capacitor as an open circuit; the reverse holds at very high frequency (EE-T1-03).
5. Complex impedance \( Z=R+jX \) with magnitude \( \sqrt{R^2+X^2} \) and angle \( \tan^{-1}(X/R) \); \( X_L=\omega L \) and \( X_C=1/(\omega C) \) (EE-T1-03).
6. Zeros of \( H(s) \) are numerator roots and poles are denominator roots; the first-order low-pass transfer function is \( H(s)=1/(1+sRC) \) (EE-T1-04).
7. In nodal analysis pick a reference node and write KCL for the others; a supernode encloses a voltage source between two non-reference nodes and adds the constraint \( V_a-V_b=V_s \) (EE-T1-05).
8. In mesh analysis write KVL for each independent mesh; a current source shared by two meshes is handled with a supermesh, which adds the constraint \( I_a-I_b=I_s \) (EE-T1-05).
9. Norton from Thevenin: \( I_N=V_{th}/R_{th} \) and \( R_N=R_{th} \); source transformation preserves what the load sees (EE-T1-06).
10. Two-port parameters: \( V=ZI \), \( I=YV \), \( V_1=AV_2-BI_2 \); for a reciprocal network \( Z_{12}=Z_{21} \) and \( AD-BC=1 \) (EE-T1-07).
11. Series second-order circuit: \( \alpha=R/2L \), \( \omega_0=1/\sqrt{LC} \); overdamped if \( \alpha>\omega_0 \), critically damped if equal, underdamped if \( \alpha<\omega_0 \) with damped frequency \( \omega_d=\sqrt{\omega_0^2-\alpha^2} \) (EE-T1-08).
12. Laplace: \( \mathcal{L}\{di/dt\}=sI(s)-i(0) \); a capacitor with initial voltage \( v_0 \) is \( 1/sC \) in series with a \( v_0/s \) source, and an inductor is \( sL \) in series with a \( Li_0 \) source (EE-T1-09).
13. Initial and final value theorems: \( f(0^+)=\lim_{s\to\infty}sF(s) \) and \( f(\infty)=\lim_{s\to0}sF(s) \), valid only when the poles of \( sF(s) \) are in the left half-plane (EE-T1-09).
14. In design, damping ratio \( \zeta=\alpha/\omega_0 \); in series RLC, increasing \( R \) raises damping and lowers \( Q \) (EE-T1-10).
15. Series resonance: \( Q=\omega_0L/R=1/(\omega_0RC) \) and \( BW=R/L \) in rad/s; parallel: \( Q=R/(\omega_0L)=\omega_0RC \) and \( BW=1/(RC) \) (EE-T1-11).
16. A first-order passive filter rolls off at 20 dB per decade past the cutoff, with a 45° phase shift there; a high-pass swaps the positions of \( R \) and \( C \) (EE-T1-12).
17. Practical aspects: a high \( Q \) gives high selectivity but, in series resonance, raises the voltage across \( L \) and \( C \) to \( Q \) times the source voltage, which can overstress components (EE-T1-13).

Common mistakes in this chapter

• ✕ When finding \( R_{th} \), only independent sources are deactivated: voltage sources are shorted and current sources opened. Dependent sources stay, and the resistance is found with a test source.
• ✕ Maximum power transfer at \( R_L=R_{th} \) gives only 50% efficiency in the equivalent circuit; it is not maximum efficiency. And \( P_{max}=V_{th}^2/(4R_{th}) \), not \( V_{th}^2/R_{th} \).
• ✕ Mixing frequency \( f \) in hertz with angular frequency \( \omega=2\pi f \) in rad/s; many wrong answers come from forgetting \( 2\pi \) in \( X_L \), \( X_C \) and \( f_0 \).
• ✕ The time constant of an RL circuit is \( L/R \), not \( RL \); for RC it is \( RC \). After one \( \tau \) the response has covered 63.2% of the total change, and it settles after about \( 5\tau \).
• ✕ At series resonance the impedance is minimum (equal to \( R \)) and current is maximum; at ideal parallel resonance the impedance is maximum and the line current is minimum. Do not swap them.
• ✕ The damping coefficient \( \alpha \) differs by topology: \( R/2L \) for series RLC and \( 1/(2RC) \) for parallel RLC; using the wrong one flips the answer between overdamped and underdamped.
• ✕ Two-port connections: series adds Z parameters, parallel adds Y parameters, and cascade multiplies ABCD matrices in the correct order; changing the order changes the result.
• ✕ Passive filters have no active gain: the voltage gain stays at or below 1 except for resonance peaking, and real amplification needs active elements. At the cutoff the gain is \( 1/\sqrt{2} \) (−3 dB), not 0.5.