Series and Parallel Circuit
Joule's Law and Power
The total voltage is
the sum of the voltage on each component.
eq 1: V0 = V1+
V2 + V3 +...+ Vn
(In this case, VT = V1+
The total resistance is equal to the sum of the
resistance on each component.
eq 2: R0 = R1
+ R2 + R3 +...+ Rn
(In this case, RT = R1 +
The total current is equal in every component.
eq 3: I0 = I1
= I2= I3= I4 =...= In
(In this case, IT = I1
First, we have to find out the total voltage using
equation 1 above, and then resistance using equation
2, and finally you can find out the current using
Total voltage is 9 + 1 + 16 + 4 = 30 V
Total resistance is 30 + 10 + 40 + 20 = 100 ohm
What is the current on A and B? ( e.g.
"1 A" )
What is the voltage on A, B and C? ( e.g.
"1 V" )
What is the resistance on C? (e.g.
What is the total resistance? (e.g.
What is total current? ( e.g. "1
The resistance is equal to the sum
of resistance on each component divided by the
product of resistance of each component.
eq 5: 1/R0 = 1/R1
+ 1/R2 +...+ 1/Rn
(In this case, 1/RT = 1/R1
The total current is equal to the sum of current
in each component.
eq 6: I0= I1
+ I2 + I3 + I4 +...+
(In this case, IT = I1
In order to find out the total voltage, we have to
find out the total resistance. Using equation 5, we
can find out the total resistance.
1/R = 1/15 + 1/15 + 1/30 = 5/30, R = 6 ohm
Using equation 4, we now know the voltage on A, B,
and C, which is 30 V each. Using ohm's law again, we
can find out the current on A, B, and C.
IA = 30/15 = 2 A,
IB = 30/15 = 2 A,
IC = 30/30 = 1 A
When you add up all the current (using equation
6), we get 5 A which is
the total current.
is the voltage on A, B and C? What is
the current on A, B, C, and D?
Total Resistance ( e.g. "1" ) ohm
Total Voltage ( e.g. "1 V" )
Total Current ( e.g. "1 A" )
Voltage on ( e.g. "10 V" )
Current on ( e.g. "0.1 A" )
The total voltage is the
voltage of series plus the voltage of parallel.
eq. 7: VT = V1
+ V2 = V1 + V3
The total resistance is the resistance of series
plus the resistance of parallel.
eq. 8: RT = R1
+ [(R2R3) / (R2 + R3)]
The total current is equal to the current on
series and to the sum of the current of parallel
eq. 9: IT = I1
= I2 + I3
First of all, we have to look at the diagram very
carefully (The order of the questions also help us
from where we have to start). Using equation
4, we know that the voltage on D is equal to C,
which is 80 V. We also know A and B have the same
voltage. Using the voltage
law, we can find out the voltage on A and B,
which is 230 - 80 = 150 V each.
Now we get all the voltages on each component.
Using ohm's law, we
can find out the current on A, B, C, and D. IA=
150/30 = 5 A; IB = 150/30 = 5 A; ID
= 80/40 = 2 A; IC = 10-2 = 8 A. The sum of
the current on A and B is equal to that of C and D (eq. 3). A+B = C+D.
You can convert joule to calories by multiplying
0.24 on joule.
In a parallel circuit, the least resistance draws
the most current and produces the most heat energy
because larger current flows through that component.
P = VI = I2R =
[W] = work (energy) / time [t] (unit of work
is joule [J] and time[t] is in second).
work or energy [joule] =
power [W] * time [t].
The unit for energy is watt-second; watt-minute;
1 watt-second =
First, we have to find out the total resistance,
and then the tatal potential difference (voltage).
Total resistance is R = 60/3 = 20 ohm.(eq.5)
And total potential difference is V= 20 * 2 = 40
V.(V=I*R) Now, we can find current on A and B. IA
= 40/30 = 4/3 A and IB = 40/60 = 2/3 A.
Power comsumption PA = (V*I) = 40 * 4/3
= 160/3 (53.3) watts; PB = 40 * 2/3 = 80/3
The heat energies are
HA = I2Rt = (4/3)2
* 30 * 10 = 1600/3 (533.3) J;
HB = (2/3)2 * 60 * 10 = 800/3
Try Chapter 14 Quiz and see how much
[Ch 11] - [Ch 12] - [Ch 13] - [Ch 14] - [Ch 15]