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Sindy asked A question to do with potential dividers made from a thermistor and a resistor?

Why does the voltage across the resistor increase when the resistance of the thermistor decrease/i.e when the temp. of the thermisor increases? Thankyou!

And got the following answer:

    __________    Voltage Divider   |        |   |        |   |     ▒ Rтнeʀмısтoʀ   |       |  Vs  ☼              |― ―――― ―→ Vouт   |       |   |     █ R   |       |   | _________   |______(Return/Ground)  With no load connected to the Vouт output. the voltage is:  Vouт = Vʀ = (Vs) • (R)  ⁄  (R + Rтнeʀмısтoʀ)   and  Vтнeʀмısтoʀ = (Vs) • (Rтнeʀмısтoʀ)  ⁄  (R + Rтнeʀмısтoʀ)   and  Vs = Vʀ + Vтнeʀмısтoʀ ≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈  from ..... Vouт = Vʀ = (Vs) • (R)  ⁄  (R + Rтнeʀмısтoʀ)  Answer 1:  as [  Rтнeʀмısтoʀ ↓ ] then [  Vʀ ↑ ] ≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈  Answer 2:  If [  Rтнeʀмısтoʀ ↓ ] as [  Temperature ↑ ]         then the thermistor has a negative temperature coefficient. ≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈  so as ... [  Temperature ↑ ] then [  Rтнeʀмısтoʀ ↓ ] and [  Vʀ ↑ ]

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