Final answer:
The charge transferred by a 9.0 V battery while doing 33 J of work is 3.7 coulombs, calculated using the equation W = V * Q and expressing the charge to two significant figures.
Step-by-step explanation:
To determine how much charge a 9.0 V battery transfers while doing 33 J of work, you can use the relationship between the voltage (V) of the battery, the work (W) done, and the charge (Q) transferred.
The equation that relates these quantities is W = V * Q, where W is work in joules, V is the potential difference in volts, and Q is the charge in coulombs.
Rearranging the equation to solve for Q gives us Q = W / V.
Substituting the values from the question, we get Q = 33 J / 9.0 V.
By performing the calculation, we find that Q = 3.67 coulombs, which we can round to two significant figures as 3.7 C.
Therefore, the battery transfers 3.7 coulombs of charge from the negative to the positive terminal while doing 33 joules of work.