# Series Circuit and Parallel Circuit

Card 1: Resistance, Current and Potential Difference in Series Circuit

## Resistance, Current and Potential Difference in Series Circuit

 Effective Resistance: R = R1 + R2 Current: I1 = I2 = I3 Potential Difference V = V1 + V2
Card 2: Resistance, Current and Potential Difference in Parallel Circuit

## Resistance, Current and Potential Difference in Parallel Circuit

 Effective Resistance: R = (R1 + R2 + R3)-1 Current: I = I1 + I2 + I3 Potential Difference V = V1 = V2 = V3
Example 1
What is the effective resistance of the connection shown in the picture below?
 a. b.

a. Effective resistance, R = 2 + 3 + 6 = 11Ω

b. Effective resistance, R = (1/5 + 1/5)-1 = 2.5 Ω

Example 2
Find the resultant resistance of the arrangement below.
 a. b.

a. Effective resistance = 3 + (1/2 + 1/2)-1 = 4Ω

b.

            {\text{Effective Resistance, }}R = (\frac{1}
{{2 + 7}} + \frac{1}
{{5 + 4}})^{ - 1}  = 4.5\Omega


Card 3: Current in Series Circuit

## Current in Series Circuit

The current flow into a resistor = the current flow inside the resistor = the current flows out from the resistor (I1 = I2 = I3)

In a series circuit, the current at any points of the circuit is the same.

Card 4: Current in Paralle Circuit

## Current in Paralle Circuit

The current flow into a parallel circuit is equal to the sum of the current in each branches of the circuit.
(I = I1 + I2)

Example:

If the resistance of the 2 resistors is the same, current will be divided equally to both of the resistor.

Example 3
In each of the diagrams below, find the reading of the ammeter.
 a. b.

a. In a series circuit, the current at any points of the circuit is the same. Therefore, the reading of the ammeter is also 0.5A.

b. Reading of the ammeter, I = 6A - 2A = 4A

Example 4

In the diagram above,

1. find the reading of the ammeter.
2. find the current flows through each of the resistors.

a.
Resistance of the (whole) circuit = 2 + 4 = 6Ω
Potential difference across the whole circuit, V = 12V
Current, I = ?

V = IR
(12) = I(6)
I = 2A

Reading of the ammeter = 2A

b.
Since in a series circuit, the current at any points of the circuit is the same. Therefore, the current flows through each of the resistors is also 2A.

Card 5: Potential Difference in Series Circuit

## Potential Difference in Series Circuit

The sum of the potential difference across individual resistor in between 2 points in a series circuit is equal to the potential difference across the two point.

V = V1 + V2

Example

Card 6: Potential Difference in Parallel Circuit

## Potential Difference in Parallel Circuit

The potential difference across all the resistor in a parallel circuit is the same.

V = V1 = V2

Example

Example 5

Find the reading of the given voltmeter(s) in the diagrams below

 a. b.

Asnwer:

a. Reading of the voltmeter, V2 = 12 - 7 = 5V

b. The potential difference across all the resistor in a parallel circuit is the same. Therefore, the reading of the voltmeter V1 is also 5V

Example 6

Find the potential difference across each of the resistors in the diagram above.

The potential difference across the whole circuit = 12V, but the potential across the 2 resistor R1 and R2 are unknown. In order to find the potential difference across the resostors, we need to find current passing through the resistors.

V = 12V, R = 6Ω, I = ?

V = IR
(12) = I(6)
I = 2A

For resistor R1,
R = 2Ω, I = 2A, V = ?

V = IR
V = (2)(2) = 4V

For resistor R2,
R = 4Ω, I = 2A, V = ?

V = IR
V = (2)(4) = 8V

The potential difference across the resistors R1 and R2 are 4V and 8V respectively.
Card 7: Potential Difference and E.M.F

## Potential Difference and E.M.F

If we assume that there is no internal resistance in the cell, the potential difference across the cell is equal to the e.m.f. of the cell.

Card 8: Potential Change in a Series Circuit

## Potential Change in a Series Circuit

V1 = V2 = V5

V3 + V4 = V5

Card 9: Potential Change in a Parallel Circuit

## Potential Change in a Parallel Circuit

V1 = V2 = V3 = V4

Example 7
Find the reading of the voltmeter in each of the circuit below.
 a. c. b. d.

a. Reading of the volmeter = e.m.f. = 3V

b. Reading of the volmeter = e.m.f. = 3V

c. Reading of the volmeter = e.m.f. = 3V

d. Reading of the volmeter = e.m.f. = 3V

Card 10: Empty Card