Series Circuit
Current in a Series Circuit
- The current at every point in a series circuit is the same.
- In the circuit in Figure X, I = I1 = 12 = I3.
Voltage in a Series Circuit
- The sum of voltage in a series circuit is equal to the voltage across the whole circuit.
- In the circuit in Figure X, V = V1 + V2 + V3.
Resistance in a Series Circuit
- As more resistors are added to the circuit, resistance will increase.
- The sum of the resistances of the bulb is equal to the total resistance of the circuit.
- For n resistors in a series, the total resistance is R = R1 + R2 + R3 ... + Rn
- where R = total resistance and n 2.
- In the circuit in Figure X, R = R1 + R2 + R3. Example:
- Bulbs X and Y with resistances 2Ω and 3Ω respectively are connected in series as shown in Figure X.
- What is the reading on the ammeter?
- Calculate the voltage across each bulb.
Advantages and Disadvantages of a Series Circuit
Advantages
- As there are no wire junctions in the circuit and all components are placed consecutively on the same path, current flow will decrease if more components are added.Thus, we can control the amount of current flow in the circuit by changing the number of components.
- The current flowing through the circuit can be increased by connecting more cells in series.
- If a component in the circuit fails, the whole system will shut down rather than run dangerously. This reduces electrical hazards (such as electric shock).
Disadvantages
- If a component in the circuit fails, then all the components in the circuit fail because the circuit has been broken.
- The more components there are in the circuit, the greater the resistance in the circuit.
- Bulbs in series will be dimmer because the electrical energy supplied is shared among more bulbs.
Parallel Circuit
Current in a Parallel Circuit
- The current from the source is the sum of the currents in the separate branches.
- In the circuit in Figure X, I = I1 + 12.
Voltage in a Parallel Circuit
- The voltage across two or more components connected in parallel to each other is the same as the voltage across the circuit.
- In the circuit in Figure X, V = V1 = V2.
Resistance in a Parallel Circuit
- As more resistors are added to the circuit, total resistance will decrease.
- Each resistor acts as an alternative path for the current.
- Thus, the more resistors connected in parallel, the more alternative paths there are for current flow.
- For n resistors in parallel, the total resistance is 1/R = 1/R1 + 1/R2 where R. = total resistance
Bulbs X and Y with resistances 2 Ω and 3Ω respectively are connected in parallel as shown in Figure X .The ammeter shows a reading of 5 A.
(a) What is the total resistance in the circuit?
(b) Calculate the voltage across the bulbs.
(c) Calculate the current flowing through each bulb.
Advantages and Disadvantages of a Parallel Circuit
Advantages
- If a component in the circuit fails, the other components can still work.This is because a parallel circuit consists of more than one branch and each component can be controlled
- When more identical bulbs are added to the circuit in parallel, the brightness of the bulbs remains the same. This is because the bulbs receive the same amount of voltage from the cells.
Disadvantages
- Cells connected in parallel will result in the same amount of voltage as one cell.
- Power supplied to the circuit will be consumed much faster if more components are connected in parallel.
Similarities and Differences between Series and Parallel Circuits
In Terms of Current
- In a series circuit, current at any point in the circuit is the same. However, current in a parallel circuit is the sum of current in its individual branches.
- From Figure X, bulbs A and B have the same brightness, that is, I = I1 = /2.
- From Figure X, if I1 > I2, bulb C is brighter than bulb D, and I = I1 + I2
- If bulbs A, B, C and D are identical, bulbs C and D will be brighter then bulbs A and B.
In Terms of Voltage
- In series circuits, voltage can be increased by adding more cells to the circuit. However, adding more cells to parallel circuits does not increase voltage throughout the circuit.
- From Figure X, bulb V3 is the brightest, that is, Vi < V2 < V3.
- From Figure X, all three bulbs have the same brightness, that is, Vi = V2 = V3.
In Terms of Resistance
- The total resistance in a series circuit is the sum of the individual resistences, given by: R = R1 + R2
- The total resistance in a parallel circuit is given by: 1/R = 1/R1 + 1/R2
