Answer
$
U_R=\frac{T}{2} I^2 R .
$
Work Step by Step
Over one cycle, the energy dissipated in the resistor is
$
U_R=\int_0^T P_R d t\\=I^2 R \int_0^T \sin ^2\left(\omega_d t-\phi\right) d t\\=\frac{T}{2} I^2 R .
$
Fundamentals of Physics Extended (10th Edition)
by Halliday, David; Resnick, Robert; Walker, Jearl
Published by
Wiley
ISBN 10:
1-11823-072-8
ISBN 13:
978-1-11823-072-5
Chapter 31 - Electromagnetic Oscillations and Alternating Current - Problems - Page 940: 89d
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