Formula Sheets Introduction to Basic Electrical Technology - Basic Electrical

 Page 1


Basic Electrical T ec hnology: In tro d uction Short
Notes for Electrical GA TE
Basic Circuit Elemen ts
Electrical circuits consist of passiv e elemen ts (resistors, capacitors, inductors) and activ e
elemen ts (v oltage and curren t sources). These elemen ts form the foundation of electrical
systems.
• Resistor : Opp oses curren t flo w, ob eys Ohm’s la w.
V = IR
where V is v oltage (V ), I is curren t (A ), R is resistance (? ).
• Capacitor : Stores energy in an electric field.
I = C
dV
dt
where C is capacitance (F ),
dV
dt
is rate of c hange of v oltage (Vs
-1
).
• Inductor : Stores energy in a magnetic field.
V = L
dI
dt
where L is inductance (H ),
dI
dt
is rate of c hange of curren t (As
-1
).
• V oltage Source : Pro vides constan t v oltage (e.g., battery).
• Curren t Source : Pro vides constan t curren t.
F undamen tal La ws
• Ohm’s La w : Relates v oltage, curren t, and resistance.
V = IR
• Kirc hhoff ’s Curren t La w (K CL) : Sum of curren ts en tering a no de equals sum of
curren ts lea ving.
?
I
in
=
?
I
out
• Kirc hhoff ’s V oltage La w (KVL) : Sum of v oltage drops around a closed lo op is
zero.
?
V =0
1
Page 2


Basic Electrical T ec hnology: In tro d uction Short
Notes for Electrical GA TE
Basic Circuit Elemen ts
Electrical circuits consist of passiv e elemen ts (resistors, capacitors, inductors) and activ e
elemen ts (v oltage and curren t sources). These elemen ts form the foundation of electrical
systems.
• Resistor : Opp oses curren t flo w, ob eys Ohm’s la w.
V = IR
where V is v oltage (V ), I is curren t (A ), R is resistance (? ).
• Capacitor : Stores energy in an electric field.
I = C
dV
dt
where C is capacitance (F ),
dV
dt
is rate of c hange of v oltage (Vs
-1
).
• Inductor : Stores energy in a magnetic field.
V = L
dI
dt
where L is inductance (H ),
dI
dt
is rate of c hange of curren t (As
-1
).
• V oltage Source : Pro vides constan t v oltage (e.g., battery).
• Curren t Source : Pro vides constan t curren t.
F undamen tal La ws
• Ohm’s La w : Relates v oltage, curren t, and resistance.
V = IR
• Kirc hhoff ’s Curren t La w (K CL) : Sum of curren ts en tering a no de equals sum of
curren ts lea ving.
?
I
in
=
?
I
out
• Kirc hhoff ’s V oltage La w (KVL) : Sum of v oltage drops around a closed lo op is
zero.
?
V =0
1
Series and P arallel Circuits
• Resistors in Series : Equiv alen t resistance.
R
eq
= R
1
+R
2
+···+R
n
where R
eq
is equiv alen t resistance (? ).
• Resistors in P arallel : Equiv alen t resistance.
1
R
eq
=
1
R
1
+
1
R
2
+···+
1
R
n
F or t w o resistors:
R
eq
=
R
1
R
2
R
1
+R
2
• V oltage Division : V oltage across a resistor in series.
V
i
= V
total
·
R
i
R
1
+R
2
+···+R
n
• Curren t Division : Curren t through a resistor in parallel.
I
i
= I
total
·
R
eq
R
i
P o w er a nd Energy
• P o w er : Rate of energy transfer.
P = VI = I
2
R =
V
2
R
where P is p o w er (W ).
• Energy : P o w er o v er time.
E = P ·t
where E is energy (J or Ws ), t is time (s ).
A C F undamen tals
• Sin usoidal V oltage : Time-v arying v oltage.
v(t)= V
m
sin(?t+?)
where V
m
is p eak v oltage (V ), ? is angular frequency (rads
-1
), ? is phase angle (rad ).
• RMS V alue : Effectiv e v alue of A C signal.
V
rms
=
V
m
v
2
˜0.707V
m
• F requency : Num b er of cycles p er second.
f =
1
T
, ? =2pf
where f is frequency (Hz ), T is time p erio d (s ).
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Page 3


Basic Electrical T ec hnology: In tro d uction Short
Notes for Electrical GA TE
Basic Circuit Elemen ts
Electrical circuits consist of passiv e elemen ts (resistors, capacitors, inductors) and activ e
elemen ts (v oltage and curren t sources). These elemen ts form the foundation of electrical
systems.
• Resistor : Opp oses curren t flo w, ob eys Ohm’s la w.
V = IR
where V is v oltage (V ), I is curren t (A ), R is resistance (? ).
• Capacitor : Stores energy in an electric field.
I = C
dV
dt
where C is capacitance (F ),
dV
dt
is rate of c hange of v oltage (Vs
-1
).
• Inductor : Stores energy in a magnetic field.
V = L
dI
dt
where L is inductance (H ),
dI
dt
is rate of c hange of curren t (As
-1
).
• V oltage Source : Pro vides constan t v oltage (e.g., battery).
• Curren t Source : Pro vides constan t curren t.
F undamen tal La ws
• Ohm’s La w : Relates v oltage, curren t, and resistance.
V = IR
• Kirc hhoff ’s Curren t La w (K CL) : Sum of curren ts en tering a no de equals sum of
curren ts lea ving.
?
I
in
=
?
I
out
• Kirc hhoff ’s V oltage La w (KVL) : Sum of v oltage drops around a closed lo op is
zero.
?
V =0
1
Series and P arallel Circuits
• Resistors in Series : Equiv alen t resistance.
R
eq
= R
1
+R
2
+···+R
n
where R
eq
is equiv alen t resistance (? ).
• Resistors in P arallel : Equiv alen t resistance.
1
R
eq
=
1
R
1
+
1
R
2
+···+
1
R
n
F or t w o resistors:
R
eq
=
R
1
R
2
R
1
+R
2
• V oltage Division : V oltage across a resistor in series.
V
i
= V
total
·
R
i
R
1
+R
2
+···+R
n
• Curren t Division : Curren t through a resistor in parallel.
I
i
= I
total
·
R
eq
R
i
P o w er a nd Energy
• P o w er : Rate of energy transfer.
P = VI = I
2
R =
V
2
R
where P is p o w er (W ).
• Energy : P o w er o v er time.
E = P ·t
where E is energy (J or Ws ), t is time (s ).
A C F undamen tals
• Sin usoidal V oltage : Time-v arying v oltage.
v(t)= V
m
sin(?t+?)
where V
m
is p eak v oltage (V ), ? is angular frequency (rads
-1
), ? is phase angle (rad ).
• RMS V alue : Effectiv e v alue of A C signal.
V
rms
=
V
m
v
2
˜0.707V
m
• F requency : Num b er of cycles p er second.
f =
1
T
, ? =2pf
where f is frequency (Hz ), T is time p erio d (s ).
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Key Notes
• Units : V oltage (V ), Curren t (A ), Resistance (? ), Capacitance (F ), Inductance (H ),
P o w er (W ), Energy (J ), F requency (Hz ).
• K CL and KVL are fundamen tal for circuit analysis in GA TE.
• Use consisten t sign con v en tions for v oltage drops and curren t directions.
• RMS v alues are used for A C p o w er calculations.
• Capacitors and inductors in tro duce time-dep enden t b eha vior in circuits.
• Use SI units for GA TE calculations.
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