Electric Circuits - Bow Valley College

Electric Circuits
Current - a flow of electric charge through a conductor.
I = q
t
I = Current (amps) A
q = Charge (coulomb) c
t = time (seconds) s
Potential difference = work done in moving a unit charge from one point to the other.
V =
Work
q
V = Potential difference or voltage
(volts)
W = Work (joules) J
V = J
Resistance - the ratio of the potential difference to the current passing through an
electrical circuit.
R = V
I
R = resistance (ohms)
Ohm's Law - the potential difference between any two points in a conductor varies
directly as the current between the two points.
V = IR
RT= R1 + R2
+ R3 . . .
IT = I1 + I2 +
I3
Series Circuits
V = Voltage (volts) V
I = Current (amps) A
R = Resistance (ohms)
Current,in a series circuit, is constant through each
resistor since only one path is provided.
VT= V1 + V2 Total voltage is equal to the addition of the voltage
C

+ V3 drops.
Units
V = A Volt = amp X ohm
Ammeter - measures current in a circuit
Voltmeter - measures the voltage drop
across part of a circuit or an entire
circuit
Resistor
Voltage source - direct current
Battery cells in series
Battery cells in parallel
Transformer
Switch open
Switch closed
Ground
Series Circuits

Find:
(a) total resistance
(b) total current
(c) Vdrop at R1, R2, R3, R4
(d) current at R3
(a) RT = R1 + R2 + R3 + R4
RT = 5.0 + 7.0 + 9.0 + 11
RT = 32
(b) VT = IRT
24V = I (32 )
I = 0.75A
(c) Vdrop at R1
Vdrop= IR
Vdrop = (0.75A) (5.0 )
Vdrop = 3.75V
Vdrop at R3
Vdrop= IR
Vdrop = (0.75A) (9.0 )
Vdrop = 6.75V
CHECK: VT = Vl + V2 +V3 +V4
VT = 3.75V + 5.25V + 6.75V + 8.25V
VT = 24V
(d) I = 0.75A (Current is constant in a series circuit)
V = IR
VT= V1 = V2 =
V3
1 = 1 + 1 +
1
RT R1 R2
Parallel Circuits
Vdrop at R2
Vdrop= IR
Vdrop = (0.75A) (7.0 )
Vdrop = 5.25V
Vdrop at R4
Vdrop= IR
Vdrop = (0.75A) (11 )
Vdrop = 8.25V
Voltage across each resistor is the same in a parallel
circuit.

R3
IT = I1 + I2 +
I3
Question 1:
In a parallel circuit the current in must equal the
current out.
Sample Parallel Circuits:
Find:
(a) total resistance
(b) total current

(c) Vdrop
(d) I1, I2, I3
(a)
(b) V = IR
(current through
each resistor)
12.0V = I (1.09 )
I = 11.0 A
(c) Vdrop= 12.0 V Voltage drop in parallel must be equal across all branches.
(d) V=I1R
12.0 V = I1 (2.0 )
I1 = 6.00 A
CHECK:
IT = I1 + I2 + I3
IT = 6.00 A + 3.00 A + 2.00 A
IT = 11.0 A
Question 2:
V = I3R
12.0 V = I3R (6.00 )
I3 = 2.00 A
V =I2R
12.0 V = I2 (4.00 )
I2 = 3.00 A

Find:
(a) RT
(b) IT
(c) I1, I2, I3
(d) V1, V2, V3
(a) 1 = 1 + 1
RT 30.0 30.0
RT = 15.0
(b) VT = ITRT
60.0 V = IT(15.0 )
IT = 4.00 A
(c) Current in line
VT = I1R
60.0 V = I1(30.0 )
I1 = 2.00 A
I2 = 2.00 A (same current in line)
CHECK:
(d) V1 = IR
V1 = (2.00 A) (10.0 )
V1 = 20.0 V
IT = I2&3 + I3
IT = 2.00 A + 2.00 A
IT = 4.00 A
VT = I3R
60.0 V = I3 (30.0 )
I3 = 2.00 A
V3 = IR
V3 = (2.00 A) (30.0 )
V3 = 60.0 V
V2 = IR
V2 = (2.00 A) (20.0 )
V2 = 40.0 V

Question 3:
Find:
(a)
(a) total resistance
(b) total current
(c) Vdrop X ----> Y
(d) Vdrop Y ----> Z
(e) Current through each resistor
I1, I2, I3, I4, I5
(b) V = IR
90.0 V = IT (3.65 )
IT = 24.7 A
(c)
CHECK: VT = 22.8 V + 67.3 V
VT = 90.0 V
(d) Current using formula V = IR

IT = I4 + I5
IT = 24.7A
CHECK: IT = I1 + I2 + I3
I4 = 13.5 A I5 = 11.2 A
Combination Series and Parallel Circuits
Question 1:
Find:
(a) total resistance
(b) total current
(c) Vdrop at parallel
(d) I through 12 resistor
(e) I through 8 resistor

(a) 1 = 1 + 1
R 12.0 8.00
R = 4.80
RT = 4.80 + 20.0 + 7.00 + 0.600
RT = 32.4
(b) V = IR
45.0 V = I (32.4 )
I = 1.39 A
c) V = IR
V = (1.39 A) (4.80 )
V = 6.67 V
(d) I through 12.0 resistor
I = 0.556 A
(e) I through 8.00 resistor
I = 0.833 A
CHECK: IT = 0.5560 A + 0.833 A
IT = 1.39 A
Question 2:
Find:
(a) total resistance
(b) total current
(c)
(d) current
through R1 & R2
(e) current
through R3 & R4

(a)
R = 3.80
RT = 3.80 + 4.00
RT = 7.80
(b) V = IR
24.0 V = IT(7.80 )
IT = 3.08A
(c)
V = IR
V = (3.08 A) (3.80 )
V = 11.7 V
(d) Current through R1 and R2
I = 2.34 A
(e) Current through R3 and R4
I = 0.731 A
CHECK: IT = 2.34 A + 0.731 A
IT= 3.08 A

Question 3:
Find
(a) total resistance
(b) total current
(c) V1, V2, V3, V4
(a) Resistances in parallel
circuits
R = 9.38
RT = 5.00 + 9.38 +
3.00 + 5.45
RT = 22.8
(b) Total current
I = 3.94 A
(c) V1 = IR
V1 = (3.94 A) (5.00 )
V1 = 19.7 V
V3 = IR
V3 = (3.94A) (3.00 )
V3 = 11.8 V
.
R = 5.45
V2 = IR
V2 = (3.94 A) (9.38 )
V2 = 37.0 V
V4 = IR
V4 = (3.94 A) (5.45 )
V4 = 21.5V

CHECK: VT = Vl + V2 +V3 +V4
VT= 90.0 V