Potential Difference Physics Example 5

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Example 5

hard
In a circuit with a 12 V12 \text{ V} battery, three resistors in series have values 2 Ω2 \text{ } \Omega, 4 Ω4 \text{ } \Omega, and 6 Ω6 \text{ } \Omega. What is the potential difference across each? Verify that they sum to the battery voltage.

Solution

  1. 1
    Total resistance: RT=2+4+6=12 ΩR_T = 2 + 4 + 6 = 12 \text{ } \Omega. Current: I=1212=1 AI = \frac{12}{12} = 1 \text{ A}.
  2. 2
    V1=IR1=1×2=2 VV_1 = IR_1 = 1 \times 2 = 2 \text{ V}; V2=IR2=1×4=4 VV_2 = IR_2 = 1 \times 4 = 4 \text{ V}; V3=IR3=1×6=6 VV_3 = IR_3 = 1 \times 6 = 6 \text{ V}.
  3. 3
    Verification: V1+V2+V3=2+4+6=12 V=VbatteryV_1 + V_2 + V_3 = 2 + 4 + 6 = 12 \text{ V} = V_{\text{battery}}. This confirms Kirchhoff's voltage law.

Answer

V1=2 V,  V2=4 V,  V3=6 VV_1 = 2 \text{ V}, \; V_2 = 4 \text{ V}, \; V_3 = 6 \text{ V}
Kirchhoff's voltage law states that the sum of potential differences around any closed loop equals zero. In a series circuit, the battery voltage divides among resistors in proportion to their resistances.

About Potential Difference

The difference in electric potential between two points, equal to the work done per unit charge moving between them.

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