The dark saturation current of a solar cell is 1.6E-8 A/m?, the cell temperature is 319 K, theshort-circuit current density is 170 A/m², Vmax is 0.476 V and the available solar radiation is724 W/m2 . The Boltzmann's gas constant is 1.381X10-23 J/K and the electronic charge is1.602X10-19 J/V. CalculateOpen-circuit voltage Voc in Volts =Current density at maximum power Imax in A/m2=Maximum power Pmax in W/m2 =% Maximum efficiency nmax =

Answered: The dark saturation current of a solar…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

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Question

The dark saturation current of a solar cell is 1.6E-8 A/m?, the cell temperature is 319 K, the
short-circuit current density is 170 A/m², Vmax is 0.476 V and the available solar radiation is
724 W/m2 . The Boltzmann's gas constant is 1.381X10-23 J/K and the electronic charge is
1.602X10-19 J/V. Calculate
Open-circuit voltage Voc in Volts =
Current density at maximum power Imax in A/m2=
Maximum power Pmax in W/m2 =
% Maximum efficiency nmax =

Expert Solution

Step 1

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Given: A solar cell in which

$T = 319 K J_{s} = 1.6 \times 10^{- 8} {A/m}^{2} J_{p h} = 170 {A/m}^{2} V_{m a x} = 0.476 V A S R = 724 {w/m}^{2}$

According to question:

a) Open circuit voltage is calculated as

$∵ V_{o c} = \frac{K T}{q} \ln (\frac{J_{p h}}{J_{s}}) \Rightarrow V_{o c} = \frac{1.38 \times 10^{- 23} \times 319}{1.6 \times 10^{- 19}} \ln (\frac{170}{1.6 \times 10^{- 8}}) \Rightarrow V_{o c} = 0.635 V$

Step 2

b) Current density at maximum power [I_max] in A/m² is calculated as

$∵ J_{m a x} = [J_{S} (e^{\frac{q V_{m a x}}{K T}} - 1) - J_{p h}] \Rightarrow J_{m a x} = [1.6 \times 10^{- 8} (e^{\frac{1.6 \times 10^{- 19} \times 0.476}{1.38 \times 10^{- 23} \times 319}} - 1) - 170] \Rightarrow J_{m a x} = - 169.47 {A/m}^{2}$

c) Maximum power[W/m²] is calculated as

$V_{m a x} = 0.476 V J_{m a x} = - 169.47 A / m^{2} ∵ P_{m a x} = J_{m a x} V_{m a x} \Rightarrow P_{m a x} = 0.476 \times - 169.47 \Rightarrow P_{m a x} = - 80.66 {W/m}^{2} -ve power means power delivered by solar cell.$

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