A 12V battery discharges for 20 minutes at a constant current of 2A and terminal voltage drops linearly from 12V to 10V. What is the total energy delivery by the battery during this time?

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  1. 26.4 KJ
  2. 12.2 KJ
  3. 120.5 KJ
  4. 24 KJ

Answer (Detailed Solution Below)

Option 1 : 26.4 KJ
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Detailed Solution

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Explanation:

Concept: The energy delivered by a battery can be calculated using the formula:

Energy = ∫ P dt

Where:

  • P is the instantaneous power delivered by the battery, given by P = V × I, where V is the terminal voltage and I is the current.
  • dt represents the time interval over which the power is delivered.

Since the voltage drops linearly from 12V to 10V over the discharge period, we can use the average voltage to simplify the calculation of energy.

Calculation:

As the voltage drops linearly from 12V to 10V, the average voltage during this period is:

Vavg = (Vinitial + Vfinal) / 2

Vavg  = (12 + 10) / 2 = 11V

Given that the discharge time is 20 minutes:

Time = 20 × 60 = 1200 seconds

Using the formula Energy = V_avg × I × Time, where:

Energy = 11 × 2 × 1200 = 26400 Joules = 26.4 kJ

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