D.C. Circuits

D.C. Circuits

Unit Outline

• 1. Recalling electric circuit symbols

• 2. How are Current, Potential Difference, and Resistance related in a Series Circuit?

• 3. How are Current, Potential Difference, and Resistance related in a Parallel Circuit?

• 4. Dealing with complex resistor combinations

• 5. Potential divider
     - a. Fixed potential divider (using fixed resistors)    - b. Variable potential divider (using rheostat)
       - i. Type 1 with rheostat connected at 2 terminals
       - ii. Type 2 with rheostat connected at 3 terminals (potentiometer)

• 6. Input Transducer
     - a. Thermistor    - b. LDR

Learning Outcomes

• Draw circuit diagrams with:   - Power sources (cell, battery, d.c. supply or a.c. supply)   - Switches   - Lamps   - Resistors (fixed and variable)   - Variable potential divider (potentiometer)   - Fuses   - Ammeters and voltmeters   - Bells   - Light-dependent resistors   - Thermistors   - Light-emitting diodes

Series Circuit Learning Outcomes

• State that the current at every point in a series circuit is the same.

• State that the sum of the potential differences in a series circuit equals the total potential difference across the whole circuit.

Parallel Circuit Learning Outcomes

• State that the sum of the currents in separate branches of a parallel circuit equals the current from the source.

• State that the potential difference across the separate branches of a parallel circuit is the same.

Effective Resistance & Ohm's Law

• Recall and apply the formulae for effective resistance of resistors in series and parallel.

• Recall the relationships including:   - $R = \frac{V}{I}$

• Apply these in calculations involving a circuit.

Recall: Electric Circuit Symbols

• Switch: ⏻

• Cell: ⚫

• Battery: ⚫⚫…

• d.c. Power Supply: ⚡

• a.c. Power Supply: ⚡✨

• Light Bulb: 💡

• Potentiometer: 🔄

• Light-Dependent Resistor (LDR): 🌞

• Ammeter: 📈

• Voltmeter: 💱

• Fixed Resistor: ≠

• Variable Resistor:럼

• Fuse: 🔒

• Thermistor: 🔥

• Light-Emitting Diode: 💡✨

Series Circuit

• Definition: In a series circuit, all components are connected in a single path.   - The current at every point is the same:
      $I_1 = I_2 = I_3 = \ldots$   - The total voltage supplied $V_\varepsilon$ is the sum across each component:
      $V_\varepsilon = V_1 + V_2 + V_3 + \ldots$   - The effective resistance is the sum of all resistances:
      $R_{eff} = R_1 + R_2 + R_3 + \ldots$

Current in Series Circuit

• Current at every point is the same due to a single path.

Potential Difference in Series Circuit

• Total potential difference across the circuit is the sum of voltages across each component:
    $V_\varepsilon = V_1 + V_2$

Effective Resistance in Series Circuit

• Total resistance equation:   $R_{eff} = R_1 + R_2$

• This can be represented in Ohm’s law as:   $V_\varepsilon = I(R_1 + R_2)$

Parallel Circuit

• Definition: In a parallel circuit, components are placed side by side (like ladder rungs).   - Total current entering the parallel branches equals the sum of the individual branch currents:   $I = I_1 + I_2 + \ldots$   - The potential difference across each branch is the same:
    $V_\varepsilon = V_1 = V_2$   - The effective resistance can be calculated from the reciprocal of resistances:   $\frac{1}{R_{eff}} = \frac{1}{R_1} + \frac{1}{R_2}$ and rewritten as:   $R_{eff} = \frac{1}{\frac{1}{R_1} + \frac{1}{R_2}}$

Summary: Series vs Parallel

Complex Resistor Combination

• Complex circuits may include both series and parallel resistors.

• Solve by isolating resistors.   1. Divide the circuit into groups.   2. Redraw with equivalent resistance.   3. Repeat until reduced to a single equivalent resistance.   4. Solve for current and voltages.

Sample Problems

• Determine equivalent resistance of a given complex circuit with resistances:   - $16.0 \, \Omega, 4.0 \, \Omega, \text{and so on}$

Potential Divider Rule

• Used to divide voltage in a circuit with resistors in series:   - $V_s = V_1 + V_2$

• The voltage across resistor R1:   - $V_1 = \frac{R_1}{R_1 + R_2} V_s$

Types of Potential Dividers

• Type 1: Rheostat - connected at two terminals, allowing for variation.

• Type 2: Potentiometer - connected at three terminals; varying resistance by slider position.

Input Transducers

• Thermistor: A device whose resistance varies with temperature. Resistance decreases with increasing temperature.   - Applications in temperature control and measurement.

• Light Dependent Resistor (LDR): Resistance decreases with increased light intensity. Used in automatic devices for light measurement.