Calculate the power absorbed by each component in the circuit shown in figure.

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Understand the Problem

The question is asking to calculate the power absorbed by each component in the provided electrical circuit diagram. This involves applying principles of electrical power calculations, such as using the formula P = VI, where P is power, V is voltage, and I is current.

Answer

$P_1 = 160 \, \text{W}, P_2 = 60 \, \text{W}, P_3 = 132 \, \text{W}, P_4 = 1210 \, \text{W}$
Answer for screen readers
  • $P_1 = 160 , \text{W}$
  • $P_2 = 60 , \text{W}$
  • $P_3 = 132 , \text{W}$
  • $P_4 = 1210 , \text{W}$

Steps to Solve

  1. Identify the components and values Determine the voltage and current for each component. From the circuit:

    • P1: Current = 10 A, Voltage = 16 V
    • P2: Voltage = 6 V (Connected parallelly)
    • P3: Current = 6 A, Voltage = 22 V
    • P4: Resistance = 0.4 Ω (We'll calculate the current through it)
  2. Calculate power absorbed by P1 Use the formula for power: $$ P = VI $$ For P1: $$ P_1 = 16 , \text{V} \times 10 , \text{A} = 160 , \text{W} $$

  3. Calculate power absorbed by P2 Using the same power formula: $$ P_2 = 6 , \text{V} \times 10 , \text{A} = 60 , \text{W} $$ (Assuming the same current flows through P2 due to parallel connection)

  4. Calculate power absorbed by P3 Applying the power formula again: $$ P_3 = 22 , \text{V} \times 6 , \text{A} = 132 , \text{W} $$

  5. Calculate current through P4 Using Ohm's Law ($ V = IR $): $$ I_4 = \frac{V}{R} = \frac{22 , \text{V}}{0.4 , \Omega} = 55 , \text{A} $$

  6. Calculate power absorbed by P4 Using the power formula: $$ P_4 = V \times I = 22 , \text{V} \times 55 , \text{A} = 1210 , \text{W} $$

  • $P_1 = 160 , \text{W}$
  • $P_2 = 60 , \text{W}$
  • $P_3 = 132 , \text{W}$
  • $P_4 = 1210 , \text{W}$

More Information

In this circuit, the power absorbed by each component is calculated based on the voltage across and the current through each component. This is essential in understanding how energy is used in electrical components.

Tips

  • Misapplying the voltage and current values in the formula. Ensure you properly identify the values corresponding to each component.
  • Assuming current is the same through all components in parallel circuits without checking the configuration.

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