A high voltage unit has an internal resistance of 50 mega ohms. On open circuit, the potential difference across its output is 3000 V. When a resistor R is connected across its output, the potential difference at the output falls to 1000 V. Calculate the resistance of R.

To calculate the resistance of resistor R, we can use Ohm's Law. Ohm's Law states that the voltage across a resistor (V) is equal to the current passing through it (I) multiplied by its resistance (R).

In this case, we know that the potential difference (V) across the unit's output is 3000 V on open circuit and 1000 V when resistor R is connected. This voltage drop occurs due to the internal resistance of the unit.

Let's assume the current passing through the unit's output (I_0) is constant in both cases. Therefore, we can calculate the resistance of R using the formula:

R = (V_0 - V) / I_0

Where:
- V_0 is the potential difference across the output on open circuit (3000 V).
- V is the potential difference across the output when resistor R is connected (1000 V).
- I_0 is the current passing through the unit's output.

However, we don't have the value for current I_0. To solve this, we can use the fact that the internal resistance of the unit creates a voltage drop across itself.

Using Ohm's Law, we can calculate the current passing through the unit's output (I_0) when there is no external resistor connected:

I_0 = V_0 / R_internal

Where:
- R_internal is the internal resistance of the unit (50 mega ohms).

Substituting the values, we have:

I_0 = 3000 V / 50e6 ohms
I_0 ≈ 0.00006 A (60 microamperes)

Now we can calculate the resistance of R using the formula mentioned earlier:

R = (V_0 - V) / I_0

R = (3000 V - 1000 V) / 0.00006 A

R ≈ 33,333.33 ohms

Therefore, the resistance of resistor R is approximately 33,333.33 ohms.