By Keiji Oenoki and Hector Judez [physics@amersol.edu.pe]

1. Series Circuit
2. Parallel Circuit
3. Series and Parallel Circuit
4. Joule's Law and Power
5. Chapter Quiz

(Series Circuit)

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

The total resistance is equal to the sum of the resistance on each component.
eq 2: R₀ = R₁ + R₂ + R₃ +...+ R_n
(In this case, R_T = R₁ + R₂)

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

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

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

(Parallel Circuit)

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/R_n
(In this case, 1/R_T = 1/R₁ + 1/R₂)

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

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

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.

I_A = 30/15 = 2 A,
I_B = 30/15 = 2 A,
I_C = 30/30 = 1 A .

When you add up all the current (using equation 6), we get 5 A which is the total current.

The total voltage is the voltage of series plus the voltage of parallel.
eq. 7: V_T = V₁ + V₂ = V₁ + V₃

The total resistance is the resistance of series plus the resistance of parallel.
eq. 8: R_T = 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: I_T = I₁ = I₂ + I₃

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. I_A= 150/30 = 5 A; I_B = 150/30 = 5 A; I_D = 80/40 = 2 A; I_C = 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.

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.

Using equation 2 we can find out total resistance of this circuit. R = 15+8 = 23 ohm; I = 230 [V] /23 [R] = 10 A

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.

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.

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

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. I_A = 40/30 = 4/3 A and I_B = 40/60 = 2/3 A.

Power comsumption P_A = (V*I) = 40 * 4/3 = 160/3 (53.3) watts; P_B = 40 * 2/3 = 80/3 (26.7) watts.

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

Try Chapter 14 Quiz and see how much you learned.