A 20 Ω resistor with temperature coefficient 0.04/°C is connected to a 24 V supply. If its temperature rises from 1.5°C to 10°C, determine: I) New resistance II) Circuit current before and after heating III) explain your answers.

The formula for resistance change with temperature is $R = R_0 [1 + \alpha \Delta T]$.

The new resistance is $\boxed{\text{26.8 } \Omega}$.

II) Circuit current before and after heating

Using Ohm's Law, $I_{initial} = \frac{V}{R_0}$.

The current before heating is $\boxed{\text{1.2 A}}$.

Using Ohm's Law, $I_{final} = \frac{V}{R}$.

The current after heating is $\boxed{\text{0.8955 A}}$.

III) Explain your answers

As the temperature of the resistor increases from $1.5^\circ C$ to $10^\circ C$, its resistance increases from $20 \, \Omega$ to $26.8 \, \Omega$. According to Ohm's Law ($I = V/R$), for a constant voltage, an increase in resistance leads to a decrease in current. Therefore, the current in the circuit decreases from $1.2 \, A$ to approximately $0.8955 \, A$.