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

$80 mA = 27 mA + A_{2}$

$A_{2} = 80 - 27 = 53 mA$

Step 3: Calculate the current through ammeter A₃

Applying Kirchhoff's first law again gives:

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

$270 mA = A_{3} + 80 mA$

$A_{3} = 270 - 80 = 190 mA$

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

$2 V + V_{1} + 12 V = 24 V$

$V_{1} = 24 - 12 - 2 = 10 V$

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

$24 V = 2 V + 8 V + (2 V_{2})$

$2 V_{2} = 24 - 2 - 8 = 14 V$

$V_{2} = \frac{14}{2} = 7 V$

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

$24 V = 2 V + V_{3}$

$V_{3} = 24 - 2 = 22 V$

Solving Problems with Kirchhoff's Laws (CIE AS Physics)

Revision Note