Tom Bruhns wrote:
"Would you then say that R3 is dissipating---0.50 watts?"

Certainly not. The two 1.5 V cells don`t put any current through each
other because they have no potential difference. The two resistors, one
in series with each cell, each drop 0.5 wolts from 1/2 amp through 1 ohm
in each case. So, there`s one volt across the common 1-ohm resistor, R3.

1 V x 1 A = 1 watt dissipated in R3.

Best regards, Richard Harrison, KB5WZI