A constant current load of 1 A is drawn from a 10 V battery for a duration of one hour during which its terminal voltage drops linearly to 9 V. What is the total energy delivered by the battery?

Concept:

When voltage varies linearly with time, the average voltage is used to calculate total energy.

Energy delivered = Current × Average Voltage × Time

Given:

• Initial voltage V_start = 10 V
• Final voltage V_end = 9 V
• Current I = 1 A (constant)
• Time t = 1 hour = 3600 seconds

Step-by-step Calculation:

Average voltage = \(\frac{V_{start} + V_{end}}{2} = \frac{10 + 9}{2} = 9.5~V\)

Energy = I × V_avg × t = 1 × 9.5 × 3600 = 34200 J = 34.2 kJ