ENG17, Sec. 2 (Montgomery)
Spring 2014
ENG17 - FINAL – Formulas
Resistors in series add:
Conductances in parallel add:
For resistors in parallel:
For 2 resistors in parallel:
Voltage Divider: For N resistors in series, the voltage in the kth resistor is given by
where Req is the series
combination of the N resistors and VS is the total voltage across all N resistors.
Current Divider: For N resistors in parallel, the current in the kth resistor is given by
where Req is the
parallel combination of the N resistors and IS is the total current through all N resistors.
Kirchoff’s Current Law (KCL): sum of all currents leaving a node is zero.
Kirchoff’s Voltage Law (KVL): sum of all voltage rises around a closed loop is zero.
Power is the rate of change of energy. Power = Voltage across element * Current through element. Power is dissipated (or
absorbed) in the element if current flows into positive terminal. Power is delivered by the element if the current flows out
of the positive terminal.
Maximum Power Transfer: load resistance (RL) = Thévenin equivalent resistance (RTH)
Input Voltage Constraint for Ideal Op Amp:
Input Current Constraint for Ideal Op Amp:
Inductors:
∫
Capacitors:
∫
Series-Connected L, C:
Parallel-Connected L, C:
Natural Response of RL Circuit:
Step Response of RL Circuit:
Natural Response of RC Circuit:
Step Response of RC Circuit:
Time Constant for RL Circuit:
Time Constant for RC Circuit:
Response of Parallel RLC:
√
Response of Series RLC:
√
√
√
Damping Response of RLC: Overdamped when
, Underdamped when
Critically Damped when
Natural Response of RLC:
,
1/2
ENG17, Sec. 2 (Montgomery)
Spring 2014
Step Response of RLC:
Sinusoidally varying voltage:
Frequency:
RMS Value of Sinusoidal Voltage:
√
Angular Frequency:
{
Phasor Transform:
}
(
Impedance:
Reactance: Imaginary part of Impedance
KVL in Frequency Domain:
KCL in Frequency Domain:
Impedances in Series:
Impedances in Parallel:
Admittance:
Mutual Inductance:
)
(G is conductance, B is susceptance, all in units of siemens (S))
√
Mutual Inductance (induced voltage):
Dot Convention for Mutually Coupled Coils: When reference direction for a current enters the dotted terminal of a coil,
the reference polarity of the voltage that it induces in the other coil is positive at its dotted terminal.
Energy Stored in Mutually-Coupled Coils:
Ideal Transformer:
Dot Convention for Ideal Transformer: (1) If coil voltages V1 and V2 are both positive or both negative at the dotmarked terminal, use a plus sign in the above voltage equation. Otherwise, use a negative sign. (2) If the coil currents I1
and I2 are both directed into or out of the dot-marked terminal, use a minus sign in above current equation. Otherwise, use
a plus sign.
Instantaneous Power:
Average (Real) Power:
Reactive Power:
Power Factor:
Reactive Factor:
Complex Power:
Apparent Power: | |
√
For Max Power Transfer:
2/2