(b) two times
Using $H = \dfrac{V^2}{R} \cdot t$, if R is halved and V remains constant, heat produced $H \propto \dfrac{1}{R}$, so H becomes two times.
Source: Chapter 11, Section 11.7 (Heating Effect of Electric Current)
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Since voltage is constant (other parameters unaltered), use $H = V^2t/R$ rather than $H = I^2Rt$. Halving R doubles H. The formula $H = I^2Rt$ would give the wrong answer here because current itself changes when R changes — always choose the formula with the quantity that stays constant (V).