ISRO EC 2023 Q.71: solution and answer

ISRO 2023 · ECQ.71 · 1 mark · MCQ

For obtaining maximum power from a solar cell, it should operate on which portion of its V-I characteristics?

(A)
Flat portion
(B)
Knee
(C)
Falling portion
(D)
None of the above

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Answer and solution

ANSWER

The solar cell should operate at the knee of its V-I characteristic, option (b).

Official answer: BSource: ISRO's revised and final answer key of 16 February 2024

The output power of a solar cell is $P = V I$ . At short circuit ( $V = 0$ ) the power is zero, and at open circuit ( $I = 0$ ) the power is also zero.
On the flat portion of the V-I curve the current is nearly constant at $I_{sc}$ , but the voltage is small, so $P = V I$ is small.
On the steep falling portion the voltage is close to $V_{oc}$ , but the current drops rapidly towards zero, so $P$ is small again.
The product $V I$ is largest at the bend (knee) between these two regions. This is the maximum power point, where $\frac{d P}{d V} = I + V \frac{d I}{d V} = 0$ , i.e. $\frac{d I}{d V} = - \frac{I}{V}$ .
The cell should therefore be operated at the knee. Options (a) and (c) each give a large current or a large voltage, but not both, so the answer is option (b).

KEY IDEA

Power is $P = V I$ , which is zero at both ends of the V-I curve. It is largest at the knee, where $d P / d V = 0$ .

WATCH OUT FOR

Choosing the flat portion because the current is highest there, or the falling portion because the voltage is highest there. Each gives only one of the two factors, not their product.

From the ISRO EC 2023 paper. Every question of this paper · The full paper (PDF, ISRO) · All 1 ISRO Optoelectronics question, with notes