A LevelPhysicsCambridge (CIE)Revision Notes10. D.C. CircuitsKirchhoff’s LawsSolving Problems with Kirchhoff's Laws

Solving Problems with Kirchhoff's Laws (Cambridge (CIE) A Level Physics): Revision Note

Exam code: 9702

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Katie M

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Solving problems with Kirchhoff's laws

  • Kirchhoff’s laws can be used to solve simple circuit problems

Worked Example

For the circuit below, state the readings of ammeters A1, A2  and A3.

WE - Kirchoff's first law question image, downloadable AS & A Level Physics revision notes

Answer:

Step 1: Calculate the current through ammeter A1

  • The 0.270 A and A1 are connected in series

  • The current entering the cell must equal the current out of it at A1 

  • Therefore A1 = 0.270 A

Step 2: Calculate the current through ammeter A2

  • From Kirchhoff's first law, the total current into a junction must equal the total current out of it

10-2-5-we-kirchhoff-step-1---cie-new

80 italic space mA italic space italic equals space 27 space mA space plus thin space straight A subscript 2

straight A subscript 2 space equals space 80 space minus space 27 space equals space 53 space mA

Step 3: Calculate the current through ammeter A3

  • Applying Kirchhoff's first law again gives:

10-2-5-we-kirchhoff-step-2---cie-new

270 space mA space equals space straight A subscript 3 space plus thin space 80 space mA

A subscript 3 space equals space 270 space minus space 80 space equals space 190 space mA

Worked Example

For the circuit below, state the readings of the voltmeters V1, V2  and V3.

All the lamps and resistors have the same resistance.

WE - kirchoff's second law question image, downloadable AS & A Level Physics revision notes

Answer:

Step 1: Calculate the potential difference shown by voltmeter V1

  • Kirchhoff's second law states that the sum of the three components is equal to the e.m.f of the supply

10-2-5-we2-kirchhoff-step-1-cie-new

2 space straight V italic space plus space straight V subscript 1 space plus thin space 12 space straight V thin space equals space 24 space straight V

straight V subscript 1 space equals space 24 space minus space 12 space minus 2 space equals space 10 space straight V

Step 2: Calculate the potential difference shown by voltmeter V2

  • Applying Kirchhoff's second law to this loop

  • Both lamps have the same resistance R and the same current I through them so they share the energy equally and have the same potential difference

10-2-5-we2-kirchhoff-step-2-cie-new

24 space straight V space equals space 2 space straight V space plus thin space 8 space straight V thin space plus thin space open parentheses 2 straight V subscript 2 close parentheses

2 straight V subscript 2 space equals space 24 space minus space 2 space minus space 8 space equals space 14 space straight V

straight V subscript 2 space equals space 14 over 2 space equals space 7 space straight V

Step 3: Calculate the potential difference shown by voltmeter V3

  • Applying Kirchhoff's second law to this loop

10-2-5-we2-kirchhoff-step-3-cie-new

24 space V space equals space 2 thin space straight V space plus space straight V subscript 3

straight V subscript 3 space equals space 24 space minus space 2 space equals space 22 space straight V

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    Katie M

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    Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.