The provided values `I=3.93A, xi = 12 V, R=3Omega` (a) The terminal voltage of the battery is same to voltage drop across the resistor `V=IR=3.93xx3=11.79V` The inner resistance the the battery, `r=<(xi-V)/(V)>R=<(12-11.79)/(11.79)>xx3=0.05Omega` (b) The power yielded by the battery `P=I xi=3.93xx12=47.1W` The power ceded to the resistor `=I^(2)R=46.3W` The continuing to be power `=(47.1-46.3)P=0.772W` is delivered to the inner resistance and cannot be offered to do beneficial work. (it is equal to `I^(2)r`).

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