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Resistors in electrical circuits IB DP Physics Study Notes

Resistors in electrical circuits IB DP Physics Study Notes - 2025 Syllabus

Resistors in electrical circuits IB DP Physics Study Notes

Resistors in electrical circuits IB DP Physics Study Notes at  IITian Academy  focus on  specific topic and type of questions asked in actual exam. Study Notes focus on IB Physics syllabus with Students should understand

  • the combinations of resistors in series and parallel circuits

Standard level and higher level: There is no Standard level content
Additional higher level: 8 hours

IB DP Physics 2025 -Study Notes -All Topics

Electric circuits

∙An electric circuit is a set of conductors (like wires) and components (like resistors, lights, etc.) connected to an electrical voltage source (like a cell or a battery) in such a way that current can flow in complete loops.
∙Here are two circuits consisting of cells, resistors, and wires.
∙Note current flowing from (+) to (-) in each circuit.


A complete circuit will always contain a cell or a battery.
∙The schematic diagram of a cell is this:

∙A battery is just a group of cells connected in series:

 
∙If each cell is 1.5 V, then the battery above is 3(1.5) = 4.5 V. What is the voltage of your calculator battery?
∙A fixed-value resistor looks like this:


∙The schematic of a fixed-value resistor looks like this:

EXAMPLE:

Draw schematic diagrams of each of the following circuits:

▶️Answer/Explanation

Solution:

Investigating combinations of resistors in series

∙Resistors can be connected to one another in series, which means one after the other.
∙Note that there is only one current I and that I is the same for all series components.

$\text{Conservation of energy tells us } q\varepsilon = qV_1 + qV_2 + qV_3.$

$\text{Thus, } \varepsilon = IR_1 + IR_2 + IR_3 \text{ from Ohm’s law } V = IR.$

$\varepsilon = I(R_1 + R_2 + R_3) \quad \text{(factoring out } I\text{)}$

$\varepsilon = I R, \quad \text{where } R = R_1 + R_2 + R_3.$

 

EXAMPLE:

Three resistors of 330 Ω each are connected to a 6.0 V battery in series.

(a) What is the circuit’s equivalent resistance?
(b) What is the current in the circuit?

▶️Answer/Explanation

SOLUTION:

(a) In series,
\[
R = R_1 + R_2 + R_3
\]
so that
\[
R = 330 + 330 + 330 = 990 \, \Omega.
\]

(b) Since the voltage on the entire circuit is 6.0 V, and since the total resistance is 990 Ω, from Ohm’s law we have
\[
I = \frac{V}{R} = \frac{6}{990} = 0.0061 \, A.
\]

Investigating combinations of resistors in parallel

  •  Resistors can also be in parallel.
  •  In this circuit, each resistor is connected directly to the cell.
  •  Thus, each resistor has the same voltage \( V \) and V is the same for all parallel components.
  •  From \( \varepsilon = V_1 = V_2 = V_3 \equiv V \) and
  • $\frac{\varepsilon}{R} = \frac{V_1}{R_1} + \frac{V_2}{R_2} + \frac{V_3}{R_3}$
  • we get
  • $\frac{V}{R_1} = \frac{V}{R_1} + \frac{V}{R_2} + \frac{V}{R_3}$
  • Thus, the equivalent resistance \( R \) is given by

 

EXAMPLE:

Three resistors of 330 Ω each are connected to a 6.0 V cell in parallel .

(a) What is the circuit’s resistance?
(b) What is the voltage on each resistor?

▶️Answer/Explanation

SOLUTION:

(a) In parallel,
\[
\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}
\]
so that
\[
\frac{1}{R} = \frac{1}{330} + \frac{1}{330} + \frac{1}{330} = 0.00909
\]
\[
\Rightarrow R = \frac{1}{0.00909} = 110 \, \Omega.
\]

(b) The voltage on each resistor is 6.0 V, since the resistors are in parallel. (Each resistor is clearly directly connected to the battery).

Ideal voltmeters – ∞ Ω resistance

 

∙Voltmeters are connected in parallel.
∙The voltmeter reads the voltage of only the component it is in parallel with.
∙The green current represents the amount of current the battery needs to supply to the voltmeter in order to make it register.
∙The red current is the amount of current the battery supplies to the original circuit.
∙In order to NOT ALTER the original properties of the circuit, ideal voltmeters have extremely high resistance (∞ Ω) to minimize the green current.

Ideal ammeters – 0 Ω resistance

∙Ammeters are connected in series.
∙The ammeter is supposed to read the current of the original circuit.
∙In order to NOT ALTER the original properties of the circuit, ideal ammeters have extremely low resistance (0 Ω) to minimize the effect on the red current.

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