(1) when a voltage of V0 = 7.48 mV is applied to a certain wire, it carries a current I0 = 0.332 A. List by name & symbol, then calculate the wire's resistance R0 in m (milliohms). Check: does your R0 give the right voltage and/or current? Watch units carefully. When expressed in designated units, qtys should not require either exponential notation or multiple zeroes.

(2) Calculate the wire's thermal power P0 in mW (milliwatts). This is the rate at which it transforms electrical energy into heat, given the conditions in Q1. Checks: put P0 and R0 through various eqns, alone or together, see if you get the right answers.

(4) Calculate the wire's new current I and thermal power P (in mW) after you raise the applied voltage to a new value V = 25.7 mV.

(6) The radius r0 for your wire is 1.48 mm, then calculate how long l0 the wire must be, given its resistance R0. Tip: convert r0 to meters before anything else. Checks: the wire should be between 10 cm and 50 m long. Does l0 give the right resistance?

(7) Version: you also have a second wire, identical in every way to the original wire, except that its radius r is 35.8% (r now equals 1.358 r0) than the original wire.

(8) Calculate the second wire's resistance R in m. Check: R can't be more than 4x larger/smaller than R0.

(9) Now suppose you wanted to heat up or cool down the original wire so that R0 became equal to R, the resistance of the second wire. Would the original wire have to be heated or cooled? Explain without eqns.

(10) Assuming that the both wires are initially at T0 = 20 C, calculate the final temperature T of the original wire when its resistance is equal to R, the resistance of the second wire. Checks: does T bear out your prediction in Q10? Does T give the right R? Lastly, a tiny temperature change can't cause a large change in resistance