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# Ohm’s Law and miserly solar modules

Working and dealing with solar photovoltaic (PV) modules daily, we all have certainly and continuously been coming across the most severe types of miserliness.

A miser is one who does not willingly share his wealth with others. Every human has this tendency to a lesser or greater extent. And not only humans: everything in this world has this property, even a PV module!

Every time you try to draw current from it, its terminal voltage drops. The more current you demand from it the lower goes the terminal voltage. In fact: everything – every system, be it electrical or mechanical or even chemical, that can offer anything to the outside world, has this property of miserliness.

Competency with PV requires an understanding of the electrophysical basis and correlations of this miserliness: Ohm’s law, which we will explain you in this article.

## Ohm’s law of miserliness

How do we quantify the miserliness of a solar module, or indeed, any electrical system? For electrical systems it is very simple. A good miser will tighten his purse strings when being asked for even for a small amount, in other words: very resistant in opening his purse.

How much does the available terminal voltage drop when we draw a small amount of current from it? This ratio of voltage drop to current drawn, that is, a resistance, is a good measure of the miserliness. This ratio is a measure of the resistance to output by the module. It is called the output resistance of the module.

It must be in series with the output current to cause a voltage drop. For this reason it is also called the ‘series resistance’, or the ‘source’ resistance. The letter symbol generally used is Rs.

This resistance, together with the open circuit voltage (Voc), will determine how much power we can expect to ‘leach’ from the miserly PV module. Open circuit voltage is the voltage on the terminals of the panel when no current is being drawn from it. Open circuit voltage is also referred by some power engineers as no-load voltage. It is something like the total assets of the miser. It keeps varying with the incident light.

We can now think of a simple circuit equivalent of the solar module. It is an (ideal) voltage source in series with an (ideal) resistance. The voltage source is the open circuit voltage Voc, and the resistance is the source resistance discussed above. Any ‘load’ connected at the terminals will come in series with Voc and Rs.

Ohm’s Law Triangle

How much current, which we abbreviate as ‘I’, will flow when a load is connected across the module?

By Ohm’s Law, the equation is:  I = [Voc/ (Rs + RL)]A, where RLis the resistance of the load device.

A case of special interest is when Ris zero Ω. This means, the terminals of the module are short-circuited. The current flowing in this condition is called the short-circuit current, Isc.  It is defined as:

Isc = Voc/ (Rs + 0)      <=>      Isc = Voc/ Rs
Therefore, the three parameters Voc, Rs, Isc are interrelated. Any two will determine the third.

Like everything in life, going into extremes will not yield optimal results, and this is no different for electricity. Too generous or too miserly people will face abuse and hate, therefore a healthy mix between the two extremes is king – and this no different for pv modules.

How to draw the equivalent circuit of a human miser? You know the answer? Please comment or send us an email at contact [at] sinovoltaics.com.

The person with the best answer will win a Solar module Quality Inspection Voucher, valued at USD 150, provided by our partner quality assurance company Kisun Solar.

Submission deadline is 15 December 2015 and the winner will be announced here – good luck!

Update 2016/01/04: over the holidays we reviewed all your great and original submissions and enjoyed them, including very creative ones (@MikeG.: “three fingers monkey”? :)). After careful reviewing all your submissions we have a final winner: congratulations Mr. Magzoub and enjoy your 150 USD Kisun Solar PV module Quality Inspection Voucher! Happy New Year 2016!

## Comment Section

3 thoughts on “Ohm’s Law and miserly solar modules

### By Magzoub on 14 November 2015

To measure the miser of a humanbeen :-
1-connect him by a big power suplay (for example a treasure).
2-connect him by a variable load (for example variable spending project).
4-connect him to a voltmeter and an Amp meater,(to read his response on the varies amount of spence).
5-but not shortcircut him(taking his treasure suddenly) this well kill him by Hart attack.
6-when the the voltmeter reading is equal to half the open voltage reading ,stop here .(reading his face responce till he become fretful ).
7-calculate his miserly =volleyed reading.(=the amount of his spense before his face become frown).

I hope I have been send the best answer.for the generous people.

### By M.A. on 20 November 2015

That is right. I see most electrical principals as applicable to all systems including the (complex) human. To test the Thevenin’s Resistance of a person ask him for a donation, or even a loan for a welfare project.
Best Wishes, M.A.

### By Steve on 9 February 2017

Hi Niclas,
Really liked the simple explanation given in the article.

Niclas is co-founder of the Sinovoltaics Group and Quality Director at 3rd party PV Quality Assurance company Kisun Solar. He is based in Shanghai and has been living and working in Asia for 9 years, including Mainland China, Taiwan, India and Iran. Niclas is PV quality specialist with extensive experience with manufacturers in Asia and has before worked on clean energy projects at UNIDO and Grameen Shakti. Connect with Niclas on LinkedIn