ENGR 240 Formulas

voltage

v = voltage (Volts)

w = energy (Joules)

q = charge (Coulombs)

current

i = current (Amperes)

q = charge (Coulombs)

t = time (seconds)

power

p = power (Watts)

w = energy (Joules)

q = charge (Coulomb)

t = time (seconds)

v = voltage (volts)

i = current (Amperes)

Voltage Controlled Voltage Source

vs = supplied voltage (volts)

u = dimensionless multiplier

vx = controlling voltage (volts)

Current Controlled Voltage Source

vs = supplied voltage (volts)

rho = multiplier (volts/ampere)

ix = controlling current (ampere)

Current Controlled Current Source

is = supplied current (ampere)

Beta = multiplier (dimensionless)

ix = controlling current (ampere)

Voltage controlled Current source

is = supplied current (ampere)

alpha = multiplier (ampere/volt)

vx = controlling voltage (volt)

Ohm’s Law

v = voltage (volts)

i = current (ampere)

R = resistance (ohm)

Conductance

G = conductance (Siemens)

R = Resistance (ohms)

Current Divider Circuit

i1 = resistor 1 current (ampere)

i2 = resistor 2 current (ampere)

is = source current (ampere)

R1 = resistor 1 (ohm)

R2 = Resistor 2 (ohm)

Voltage Division

vj = voltage of resistor in question (volt)

Rj = resistor in question (ohm)

i = current (ampere)

Req = equivalent resistance (ohm)

vs = voltage source (volt)

Current Division

ij = current of resistor in question (ampere)

Rj = resistor in question (ohm)

v = voltage (volt)

Req = equivalent Resistance (ohm)

Wheatstone Bridge

Rx = unknown resistance (ohm)

R1,R2 = resistors of Wheatstone bridge (ohm)

R3 = variable resistor of Wheatstone bridge (ohm)

Delta to Wye Conversion

R1,R2,R3 = Wye Resistors (ohm)

Ra,Rb,Rc = Delta Resistors (ohm)

Wye to Delta Conversion

R1,R2,R3 = Wye Resistors (ohm)

Ra,Rb,Rc = Delta Resistors (ohm)

Equivalent Resistance (Series)

Req = equivalent resistance

R1,R2,Rk = resistors in series connection (ohm)

Equivalent Resistance (Parallel)

Req = equivalent resistance (ohm)

R1,R2,Rk = resistors in parallel connection (ohm)

Two resistors in parallel

Req = equvialent resistance (ohm)

R1, R2 = two resistances connected in parallel (ohm)

Voltage Divider Circuit

v1 = voltage of resistor 1(volt)

v2 = voltage of resistor 2 (volt)

R1 = resistor 1 (ohm)

R2 = resistor 2 (ohm)

vs = voltage source (ohm)

Current Divider Circuit

i1 = current of resistor 1 (ampere)

i2 = current of resistor 2 (ampere)

R1 = resistor 1 (ohm)

R2 = resistor 2 (ohm)

is = current source (ampere)

Condition of Equivalence

is = current source

vs = voltage source

R = resistor in both circuits

Thevenin/Norton Resistance

RTh = Thevenin Resistance (ohms)

VTh = Thevenin Voltage (volt)

isc = short circuit current (ampere)

Maximum Power Transfer

pmax = maximum power (watt)

VTh = Thevenin Voltage (volts)

RL = Load Resistance (Ohm)

Inverting Amplifier Equation

vo = output voltage (volt)

Rf/Rs = scaling factor

vs = input voltage (volt)

Inverting Summing-Amplifier Equation

vo = output voltage (volt)

Rf = feedback resistance (ohm)

va,vb,vc = input voltages (volt)

Ra,Rb,Rc = input resistances (ohm)

Non-Inverting Amplifier Equation

vo = output voltage (volt)

Rs = source resistance (ohm)

Rf = feedback resistance (ohm)

vg = source voltage (ohm)

Difference-Amplifier Equation

vo = output voltage (volt)

Ra,Rb,Rc,Rd = input resistances (ohm)

va,vb = input voltages (volt)

Simplfied Difference-Amplifier Equation

vo = output voltage (volt)

Ra,Rb = input resistances (ohm)

va,vb = input voltages (volt)

Common Mode Rejection Ratio (CMRR)

CMRR = Common Mode Rejection Ratio

Adm = differential mode gain

Acm = common mode gain

Common Mode Gain

Ra,Rb,Rc,Rd = input resistances (ohm)

Differential Mode Gain

Ra,Rb,Rc,Rd = input resistances (ohm)

Differential mode input voltage

vdm = differential mode voltage

vb,va = input voltages

Common mode input voltage

vcm = common mode voltage

vb,va = input voltages

input voltages in terms of common mode and differential mode

va,vb = input voltages

vcm = common mode voltage

vdm = differential mode voltage

Inductor v-i Equation

v = voltage (volts)

L = inductance (henrys)

di/dt = rate of change of current over time

inductor i-v equation

i(t) = current

L = inductance (henrys)

t = time

t0 = initial time

power in an inductor

p = power (watts)

L = inductance (henrys)

i = current (amperes)

di/dt = rate of change of current over time

Energy in an inductor

w = energy (joules)

L = inductance (henrys)

i = current (amperes)

capacitor i-v equation

i = current (amperes)

C = capacitance (farads)

dv/dt = rate of change of voltage over time

capacitor v-i equation

v(t) = voltage

C = capacitance (farads)

t = time

t0 = initial time

i = current (amperes)

capacitor power equation

p = power (watts)

v = voltages (volts)

i = current (amperes)

C = capacitance (farads)

dv/dt = rate of change of voltage over time

capacitor energy equation

w = energy (joules)

C = capacitance (farads)

v = voltage (volts)

Combining Inductance in Series

Leq = equvialent Inductance

i = number of inductors in series

COMBINING INDUCTORS AND THEIR INITIAL CURRENTS IN PARALLEL

Leq = equivalent inductance

i = number of inductors in parallel

i(t0) = initial current

COMBINING CAPACITORS AND THEIR INITIAL VOLTAGES IN SERIES

Ceq = equivalent capacitance

i = number of capacitors in series

v(t0) = initial voltage

Combining Capacitors in parallel

Ceq = equivalent capacitance

i = number of capacitors in parallel