The rule of thumb is roughly constant up to about one-third of the capacitors reactance. So for R from 0 to about 5000 ohms we can assume close to 16ma current. This makes the output voltage easier to calculate.
Output voltage roughly 0.016 times the resistance.
If there is an LED then we can assume the resistance is the voltage of the LED divided by 0.016, so for a 1.6v LED that means it will be about 100 ohms.
When you place a capacitor in front of a bridge rectifier on 240v you are producing what is called a CONSTANT CURRENT GENERATOR or CONSTANT CURRENT CIRCUIT.
In your case the constant current is 15mA. This 15mA will flow through a short circuit, a LED or a 1k resistor. ... The actual current will depend on the voltage developed across the load.