l. Resistive conductors tend to heat up when current flows through them. The temperature of the conductor typically depends on the amount of current it carries, where a higher current leads to a higher temperature. Additionally, the resistivity of a metallic conductor increases with increasing temperature. Therefore, the resistance of a piece of metal will generally increase if the current in the metal increases. This effect is usually negligible if the temperature of a circuit element does not vary too much during its operation. However, this effect can be significant in circuit elements that experience large temperature variations, like incandescent light bulbs and the heating elements in a toaster. The main component in an incandescent light bulb is a coiled filament of tungsten that is 580 mm long with a diameter of 46 pm. At 20C, tungsten has a resistivity of 5.25 x 10'8 Q - 111. Its temperature coefficient of resistivity is 0.0045 (C)'1, and this remains accurate even at high temperatures. (a) Initially, the temperature of the filament is 20C and there is no current flowing through it. What is the resistance ofthe light bulb under these conditions? {bl If a voltage is applied across the terminals of the light bulb, current begins to flow through it. The temperature T of the filament increases linearly with the currentf through it, according to the equation TU) : (2500C -A'1)I + 20C. What is the current through the light bulb when the voltage across its terminals is 120 V? (Hint: Use the equation given in this part to determine the resistance of the light bulb as a function of current. Substitute that result into the equation V = IR, and solve for the current I.) {c} What is the temperature of the filament when the voltage across it is 120 V? (d) What is the resistance of the light bulb when the voltage across its terminals is 120 V? Compare your result with the room-temperature, zero-current resistance you found in Part (a)