I am confused by the meaning of the resistor, the circuit is not open/broken, which is not in the same situation in the first picture I posted.
So in this setup, IF the circuit is complete in the first place, current will NOT flow from 5V to the 10k resistor but going to PIN 1 of DHT11 straight away, due to the high resistance of the resistor. AND shouldn't PIN 2 outputting current right away INTERNALL(tapping into the current from VCC within the sensor)
A 3-PIN DHT11 doesn't need a pull-up resistor while a 4-PIN one DO require one.
Why is it necessary to add a pull up resistor for 4 Pin DHT11?
Hope that the following conceptual diagram (Fig-1) of 4-pin DHT11connected with UNO will answer to some of your questions:
Figure-1:
1. Q1 is an open collector transistor. So, to generate pulses at DPin-2 in response to the signal at base of Q1, there must be a pull-up resistor (R) at C-point of the transisitor. This is basic electronics.
2. There is an internal pull-up resistor (Rip) inside the Arduino UNO, and this resistor comes in picture when DPin-2 is configured as an input line. The following code can be put under setup() function to connect the Rip (S1 will be closed) and then the external pull-up (R) will not be needed any more. (Note that Rip has the value 20k-50k, and it may work work and may not with DHT11.)