Simple Circuits

P3.2-1 Series circuit

For components connected in series:

1. Current is the same (I₁ = I₂);
2. Addition of PD across all of them, is equal to the PD of the cell (V_T = V₁ + V₂ + V₃)
3. Total resistance is equal to the sum of all of them: R_T = R₁ + R₂ + R₃ + …

P3.2-2 Parallel Circuit

For components connected in parallel:

1. PD is the same across them (V₁ = V₂ = V₃ = V_T);
2. Current is shared (I₁ = I₂ +  I₃ + I₄);
3. Total resistance is found by this formula:

P3.2-3 Circuit symbols

Symbol	Name	Function
	Switch Open	To stop electric current
	Switch Closed	To allow the current to flow
	Cell	Supply electric energy (PD), longer side shows +
	Battery	More than one cell
	Filament Lamp	Produce light (and heat)
	Fuse	Metal inside the fuse melts if current exceeds than a certain value and stops the current
	Voltmeter	Measures PD across a component
	Ammeter	Measures current
	Resistor	Creates friction against current
	Diode	Allows current in one direction only
	LED	Light Emitting Diode
	Variable Resistor	A resistor that we change its resistance
	Thermistor (NTC) NTC: Negative Temperature Coefficient	A variable resistor sensitive to temperature NTC: as temperature goes up, resistance goes down
	LDR	Light dependent resistor: as light intensity goes up, resistance goes down

P3.2-3 Ohm’s Law

P3.2c

Resistance

As electrons are pushed around a circuit by the cell, they collide with metal ions of the resistor (or any conductor). This increases the temperature of the resistor and makes the ions to vibrate more which in turn will increase the number of collisions and hence will increase the resistance! 

Sometimes we use this heat: e.g. in electric heaters, and filament lamp gets so hot that emits light!

Ohm’s Law:

P3.2-4 I-V Graphs

In the graphs below, resistance is the inverse of the gradient.

The resistance of a filament lamp should be calculated from instantaneous values of I and V, not the gradient of the graph (means drawing the tangent does not work here!), because according to Ohm's law resistance is the ratio, not the slope.

Design a circuit to study I-V graph of different components

Connect the voltmeter across the component that we study.

By decreasing the resistance of the variable resistor, the current in the circuit increases. 

With any change in resistance, we can read a new pair of value for PD and current:

I-V characteristic graph of different components:

A linear component is the one with linear I-V graph!

A diode starts to allow current once the PD across reaches about 0.6 v.

Adding a resistor in series increases the total resistance, as the current has to go through an extra component!

Adding a resistor in parallel decreases the total resistance, as an extra path is created for the current. 

Q1. In the circuit below:

R₁ = 2 Ω

R₂ = 4 Ω

PD of the cell is 12 v.

Calculate the current I₁, and readings of V₁ and V₂.

To find current, we should know electrons feel the total resistance in the circuit before they come out of the cell! 

This is a series circuit so the current is the same anywhere! 

So first step is to find the total resistance:

Series circuit:

Now we can simplify the circuit to find the current

Use Ohm’s law:

Now by knowing the current in each of resistors R₁ and R₂ we can find PD across each them:

Ohm’s Law:   and

There is another way to find V₂:

Total PD (energy per unit charge) provided to the circuit is 12 v, of which 4 v is spent by R₁. So the leftover is given to R₂: 12 – 4 = 8 v

Q2. In the circuit below:

R₁ = 3 Ω

R₂ = 6 Ω

PD of the cell is 12 v.

Calculate the currents I₁, I₂ and I₃ and determine the readings of V₁ and V₂.

To find the current in the cell, first we need to find the total resistance in the circuit:

Parallel circuit:

So we can simplify the circuit:

Use Ohm’s law:

Components connected in parallel have the same PD: V₁ = V₂ = 12 v

So we can find the current in each of resistors R₁ and R₂:

and

There is another way to find I₃:

 I_{1 =} I_{2 +} I₃ so I₃ = 6 – 4 = 2 A

Circuit below can be used to investigate variation of resistance of thermistor with temperature, or LDR with light intensity:

For both of these components a graph like the following can be seen:

A thermistor is made of a semiconductor. Semiconductors have more free electrons when heated, hence resistance of a thermistor decreases as temperature increases! 

P3.2-5 Electric Power

P3.2L

1. Power is energy transferred over time (see P2.2n).
2. PD is energy over charge (see P3.1e)
3. Charge is current times time (see P3.1d)

Q1. An electric kettle draws a current of 10 A from the mains supply. There is 1 kg of water in the kettle. If the kettle is on for 2 minutes. 

1. Calculate the temperature change of the water;
2. Calculate the resistance of the kettle;
3. Explain why in reality the temperature change is less than the value you calculated in part a.

Mains supply PD = 230 v

Specific heat capacity of water = 4200 J/kg^oC

C) Some of the energy is wasted to warm up the kettle itself, and some is transferred to the surroundings.

Q2. A hairdryer has a power rating of 1.5 kW. If the mains supply is 230 v. Calculate:

1. The current in the hairdryer;
2. The resistance of the hairdryer.