In full sunlight, a solar cell has a short circuit current of 75 mA and a current of 70 mA for a terminal voltage of 0.6 V with a given load. The Thevenin resistance of solar cell is

Understanding Thevenin Resistance for a Solar Cell

This problem asks us to find the Thevenin resistance of a solar cell based on its performance under specific conditions. The Thevenin equivalent circuit is a way to simplify a complex electrical network into a single voltage source and a single series resistance.

Given Information

- Short circuit current, **$I_{sc}$ = 75 mA = 0.075 A
- Current, $I$ = 70 mA = 0.070 A
- Terminal voltage, $V$ = 0.6 V

Thevenin Model Explanation

A solar cell, when analyzed using Thevenin's theorem, can be represented by a Thevenin voltage source ($V_{th}$ ) in series with its Thevenin resistance ($R_{th}$ **).

- The short-circuit current ($I_{sc}$) is the maximum current the cell can produce when the terminals are shorted (load resistance is zero). In this scenario, the current flows directly from the voltage source through the Thevenin resistance. Thus, we can write: $$I_{sc}=\frac{V_{th}}{R_{th}}$$ This can be rearranged to find the Thevenin voltage: $$V_{th}=I_{sc}\cdot R_{th}$$
- When a load is connected, resulting in a current $I$ and a terminal voltage $V$, this voltage $V$ is measured across the load. The voltage source $V_{th}$ minus the voltage drop across the internal Thevenin resistance ($I\cdot R_{th}$) equals the terminal voltage $V$. So: $$V=V_{th}-I\cdot R_{th}$$

Calculating Thevenin Resistance

We can find the Thevenin resistance by substituting the expression for **$V_{th}$ ** from the first equation into the second equation:

$$V=(I_{sc}\cdot R_{th})-(I\cdot R_{th})$$

Factor out **$R_{th}$ **:

$$V=R_{th}(I_{sc}-I)$$

Now, we can solve for **$R_{th}$ **:

$$R_{th}=\frac{V}{I_{sc}-I}$$

Step-by-Step Calculation

Substitute the given values into the derived formula:

- **$V$ = 0.6 V
- $I_{sc}$ = 0.075 A
- $I$ ** = 0.070 A

Calculation:

$$R_{th}=\frac{0.6\text{ V}}{0.075\text{ A}-0.070\text{ A}}$$

$$R_{th}=\frac{0.6\text{ V}}{0.005\text{ A}}$$

$$R_{th}=120\Omega$$

Therefore, the Thevenin resistance of the solar cell is **120 $\Omega$ **.