calculate current in the follwing fig
Answers
practice problem 1
Determine the following quantities for each of the two circuits shown below…
the equivalent resistance,
the total current from the power supply,
the current through each resistor,
the voltage drop across each resistor, and
the power dissipated in each resistor.
Boring series circuit
Boring parallel circuit
solution
Follow the rules for series circuits.
Resistances in series add up.
RT = R1 + R2 + R3
RT = 20 Ω + 30 Ω + 50 Ω
RT = 100 Ω
Total current is determined by the voltage of the power supply and the equivalent resistance of the circuit.
IT = VT/RT
IT = 125 V/100 Ω
IT = 1.25 A
Current is constant through resistors in series.
IT = I1 = I2 = I3 = 1.25 A
The voltage drops can be found using Ohm's law.
V1 = I1R1
V1 = (1.25 A)(20 Ω)
V1 = 25.0 V
V2 = I2R2
V2 = (1.25 A)(30 Ω)
V2 = 37.5 V
V3 = I3R3
V3 = (1.25 A)(50 Ω)
V3 = 62.5 V
Verify your calculations by adding the voltage drops. On a series circuit they should equal the voltage increase of the power supply.
VT = V1 + V2 + V3
125 V = 25.0 V + 37.5 V + 62.5 V
125 V = 125 V
We're good, so let's finish.
There are three equations for determining power. Since we have three resistors, let's apply a different equation to each as an exercise.
P1 = V1 I1
P1 = (25.0 V)(1.25 A)
P1 = 31.250 W
P2 = I22R2
P2 = (1.25 A)2(30 Ω)
P2 = 46.875 W
P3 = V32/R3
P3 = (62.5 V)2/(50 Ω)
P3 = 78.125 W
In a series circuit, the element with the greatest resistance consumes the most power.
Follow the rules for parallel circuits.
Resistances in parallel combine according to the sum-of-inverses rule.
1 = 1 + 1 + 1
RT R1 R2 R3
1 = 1 + 1 + 1
RT 20 Ω 100 Ω 50 Ω
1 = 5 + 1 + 2
RT 100 Ω 100 Ω 100 Ω
1 = 8
RT 100 Ω
RT = 100 Ω = 12.5 Ω
8
Total current is determined by the voltage of the power supply and the equivalent resistance of the circuit.
IT = VT/RT
IT = 125 V/12.5 Ω
IT = 10 A
(Note: we'll answer part iv before part iii.) On a parallel circuit, each branch experiences the same voltage drop.
VT = V1 = V2 = V3 = 125 V
The current in each branch can be found using Ohm's law.
I1 = V1/R1
I1 = (125 V)/(20 Ω)
I1 = 6.25 A
I2 = V2/R2
I2 = (125 V)/(100 Ω)
I2 = 1.25 A
I3 = V3/R3
I3 = (125 V)/(50 Ω)
I3 = 2.50 A
Verify your calculations by adding the currents. On a parallel circuit they should add up to the current from the power supply.
IT = I1 + I2 + I3
10 A = 6.25 A + 1.25 A + 2.50 A
10 A = 10 A
Good, it works.
Again as an exercise, use a different equation to determine the electric power of each resistor.
P1 = V1I1
P1 = (125 V)(6.25 A)
P1 = 781.25 W
P2 = I22R2
P2 = (1.25 A)2(100 Ω)
P2 = 156.25 W
P3 = V32/R3
P3 = (125 V)2/(50 Ω)
P3 = 312.50 W
In a parallel circuit, the element with the least resistance consumes the most power
total resistance = 1\r1 + r2 + r3 + 1\ r4 + r5
= 1\3.6 + 6 + 3 + 1\ 1 + 3
= 1\12.6 + 1\4
= 20 + 63\ 252
= 83\252
= 0.32 ohm
V = IR
4.5 = I * 0.32
I = 4.5\0.32
therefore I = 14.06
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