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The question asks for the resistance \( R \) that will provide a current of 25 mA to the LED, assuming the LED's turn-on voltage is 2 V.

### Step 1: Understanding the Circuit
- The circuit consists of a voltage source \( V_{in} \), a resistor \( R \), and an LED in series.
- The voltage drop across the LED is given as 2 V when it is turned on.
- The current flowing through the circuit, which also flows through the resistor and LED, is 25 mA (or 0.025 A).

### Step 2: Applying Ohm's Law
Ohm's Law is given by:
\[
V = IR
\]
where:
- \( V \) is the voltage across the resistor,
- \( I \) is the current through the resistor,
- \( R \) is the resistance.

### Step 3: Determine the Voltage Across the Resistor
The voltage across the resistor \( V_R \) can be found by subtracting the LED's voltage from the total input voltage \( V_{in} \):
\[
V_R = V_{in} - V_{LED}
\]
where:
- \( V_{LED} = 2 \) V (given),
- \( V_{in} \) is the total input voltage from the source.

### Step 4: Calculate the Resistance \( R \)
Using Ohm's Law:
\[
R = \frac{V_R}{I} = \frac{V_{in} - V_{LED}}{I}
\]
Substitute the given values:
\[
R = \frac{V_{in} - 2 \text{ V}}{0.025 \text{ A}}
\]
To find the resistance, we need the value of \( V_{in} \).

### Missing Information
The problem does not specify the input voltage \( V_{in} \). Assuming \( V_{in} \) is a typical value (e.g., 5 V or 9 V), the resistance can be calculated. If \( V_{in} \) is known, we can plug it into the equation to find \( R \).

Would you like to provide the input voltage or proceed with an assumption to calculate the resistance?

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**Questions for Further Thought:**
1. What effect does changing the input voltage \( V_{in} \) have on the required resistance \( R \)?
2. How does the turn-on voltage of the LED affect the circuit design?
3. What happens if the resistance \( R \) is too low or too high?
4. Can you determine the power dissipation in the resistor once \( R \) is known?
5. How would the circuit be affected if multiple LEDs were used in series?

**Tip:** When dealing with LEDs, always check the current rating to avoid exceeding the maximum current, which could damage the LED.

Find the resistance R that will provide a current of 25 mA to the LED. Assume that the LED turn-on voltage is 2 V.

Learn how to calculate the resistance required in a series circuit to provide 25 mA of current to an LED with a turn-on voltage of 2 V. The problem involves applying Ohm's Law and understanding series circuit behavior. Suitable for undergraduate students.

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