Chapter 14
  The CircuitBasic Circuit
 

 

  1. Series Circuit
  2. Parallel Circuit
  3. Series and Parallel Circuit
  4. Joule's Law and Power
  5. Chapter Quiz
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  There are basically three types of circuit -- series, parallel, and series and parallel circuit.
  Series Circuit:
Series Circuit
  Parallel Circuit:
Parallel Circuit

 

  Section
Section 1. Series Circuit
  Check!
Series Circuit

(Series Circuit)

The total voltage is the sum of the voltage on each component.
eq 1: V0 = V1+ V2 + V3 +...+ Vn
(In this case, VT = V1+ V2)

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 + R2)

The total current is equal in every component.
eq 3: I0 = I1 = I2= I3= I4 =...= In
(In this case, IT = I1 = I2)

  Example 1.
 
Example 1 a We have a series circuit like this. What is the total voltage, resistance and current?

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 equation 3.

Total voltage is 9 + 1 + 16 + 4 = 30 V
Total resistance is 30 + 10 + 40 + 20 = 100 ohm

Example 1 b Using ohm's law, I = V / R, then we can find out the total current.
I = 30 / 100 = 0.3 A

 

 
Example problem. 1
Example Problem 1 The circuit is series.

What is the current on A and B? ( e.g. "1 A" )

A -

B -

What is the voltage on A, B and C? ( e.g. "1 V" )

A -

B -

C -

What is the resistance on C? (e.g. "1") ohm

What is the total resistance? (e.g. "1") ohm

What is total current? ( e.g. "1 A" )

 

  Section
Section 2. Parallel Circuit.
  Check!
Parallel Circuit

(Parallel Circuit)

The total voltage is equal in every component.
eq 4: V0 = V1= V2= V3 =...= Vn
(In this case, VT = V1= V2)

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 + 1/R2)

The total current is equal to the sum of current in each component.
eq 6: I0= I1 + I2 + I3 + I4 +...+ In
(In this case, IT = I1 + I2)

  Example 2.
 

Example of parallel circuit

If you have a parallel circuit like this, what is the total resistance and voltage? And voltage and current on A, B, and C?

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

Parallel circuit reduced to series circuit Then using ohm's law,V = I R, we can find out the total voltage.
V = 5 * 6 = 30 V

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.

 

 
Example problem. 2
Example 2 What is the total resistance, voltage, and current?

What 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" )

A -

B -

C -

Current on ( e.g. "0.1 A" )

A -

B -

C -

D -

 

  Section
Section 3. Series - Parallel Circuit.




  Check!
Series-Parallel; many circuit are both series and parallel.

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 circuit.

eq. 9: IT = I1 = I2 + I3

Series and parallel circuit

 

  Example 3.
 
Series and parallel circuit What is voltage on A, B, and D?
What is current on A, B, C, and D?
What is resistance on C?
What is total current and resistance?

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.

Resistance of A and B The resistance of A+B is 15 ohm (eq. 2) The resistance on C is R = 80 [V] /8 [IC]= 10 ohm. Therefore, the resistance of C+D is 8 ohm.
Total resistance Using equation 2 we can find out total resistance of this circuit.
R = 15+8 = 23 ohm; I = 230 [V] /23 [R] = 10 A

 

  Section
Section 4. Joule's Law and Power
  Check!
The heat energy produced by a resistor is

H = I2Rt

where:

  • H is heat energy in joule,
  • I is the current in A,
  • R is the resistance in ohm, and
  • t is time in second.

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.

  Check!
The rate of using or supplying energy is called power [P]. The power consumption of a resistor is

P = VI = I2R = V2/R

where:

  • [P] is power in watts,
  • [V] is voltage through resistor in volts,
  • [I] is current through resistor in ampere, and
  • [R] is resistance in ohms.


  Check!
Also,

Power [W] = work (energy) / time [t] (unit of work is joule [J] and time[t] is in second).

Therefore,

work or energy [joule] = power [W] * time [t].

The unit for energy is watt-second; watt-minute; and watt-hour.

1 watt-second = 1 joule

 

  Example 4.
 
A parallel circuit What is the power consumption of the resistor A and B? (in watts; [W])
What the heat energy produced on A and B if it is used in 10 second?
(in joule; [J])

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 (26.7) watts.

The heat energies are
HA = I2Rt = (4/3)2 * 30 * 10 = 1600/3 (533.3) J;
HB = (2/3)2 * 60 * 10 = 800/3 (266.7) J.

 

  Section
Section 5: Chapter Quiz

Try Chapter 14 Quiz and see how much you learned.


[Ch 11] - [Ch 12] - [Ch 13] - [Ch 14] - [Ch 15]