Sketch A Circuit Diagram Showing Two Resistors P And Q Conne

Sketch A Circuit Diagram To Show Two Resistors P And Q Connected In Se

Sketch a circuit diagram to show two resistors P and Q connected in series with a battery composed of two cells connected in series. Resistor P has a resistance of 4 ohms, resistor Q has a resistance of 2 ohms, and each cell has a potential difference of 1.5V. Calculate the total potential difference of the two cells, the total resistance of the two resistors, the current in the circuit, and the potential difference across the resistors.

Paper For Above instruction

The circuit described involves two resistors, P and Q, connected in series to a battery made of two cells connected in series. This configuration is essential to understand the behavior of current and voltage distribution in simple electrical circuits.

Sketching the Circuit Diagram

The circuit diagram consists of a battery, two resistors connected in series, and a complete closed loop. The battery comprises two cells, each providing 1.5V, connected end-to-end to produce a total emf of 3V. From the positive terminal of the combined battery, a wire leads to resistor P (4 ohms). The resistor P is connected in series with resistor Q (2 ohms), and the circuit is completed by connecting back to the negative terminal of the battery, forming a closed loop.

In the diagram, the components should be labeled as follows: the battery (2 cells in series), resistor P (4Ω), resistor Q (2Ω). The current flows clockwise from the positive terminal of the battery, through resistor P, then resistor Q, and back to the negative terminal.

Calculations

Total Potential Difference of the Two Cells

The total emf of the battery is the sum of the individual cell potentials, as they are connected in series:

• Total EMF, E_total = 1.5V + 1.5V = 3V

Total Resistance of the Two Resistors

Resistors in series add directly:

• R_total = R_P + R_Q = 4Ω + 2Ω = 6Ω

Current in the Circuit

Using Ohm’s Law (V = IR), the current in the circuit (I) is calculated by dividing the total emf by the total resistance:

• I = E_total / R_total = 3V / 6Ω = 0.5 A

Potential Difference Across the Resistors

The potential difference across each resistor is proportional to its resistance, given by V = IR.

• Potential difference across resistor P:
• V_P = I × R_P = 0.5 A × 4Ω = 2V
• Potential difference across resistor Q:
• V_Q = I × R_Q = 0.5 A × 2Ω = 1V

Note that the sum of the potential differences across the resistors equals the total emf of the battery (2V + 1V = 3V), confirming the consistency with Kirchhoff’s Voltage Law.

Understanding this circuit demonstrates how voltage divides among resistors in series and emphasizes the linear relationship described by Ohm’s Law. The current remains constant throughout the series circuit, and the potential difference divides according to resistance values, which is critical knowledge in designing and analyzing electrical circuits.

References

• Resistor Series and Parallel Circuits. (2021). Electronics Tutorials. https://www.electronics-tutorials.ws/resistor/res_4.html
• Ohm's Law. (2020). Khan Academy. https://www.khanacademy.org/science/physics/circuits-topic/resistors/a/ohms-law
• Basic Electricity and Electronics. (2018). National Instruments. https://www.ni.com/en-us/innovations/education/what-is-electrical-current.html
• Introduction to Circuits. (2019). Physics Classroom. https://www.physicsclassroom.com/class/estatics/Lesson-1/Current
• Fundamentals of Electric Circuits. (2017). Alexander and Sadiku. McGraw-Hill Education.
• Series and Parallel Circuits. (2022). HyperPhysics. Georgia State University. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/serpar.html
• Electrical Resistance and Power. (2018). Purdue University. https://purdue.edu/engineering/eas/academic_units/electrical_and_computer_engineering/ece-products-resources/undergraduate-resources/circuit-theory.html
• Application of Kirchoff’s Laws. (2020). Stanford Education. https://stanford.edu/~saksham/physics/kirchhoffs_laws.html
• Resistor Calculations and Applications. (2019). All About Circuits. https://www.allaboutcircuits.com/technical-articles/basic-resistor-commands-and-their-functions/
• Electric Current and Resistance. (2016). Britannica. https://www.britannica.com/science/electric-current