Physics, 20.09.2020 14:01 linreaburg
A 100-W (watt) light bulb has resistance R=143Ω (ohms) when attached to household current, where voltage varies as V=V0sin(2πft), where V0=110 V, f=60 Hz. The power supplied to the bulb is P=V2R J/s (joules per second) and the total energy expended over a time period [0,T] (in seconds) is
Answers: 1
![V = V_o sin [2 \pi ft]](/tpl/images/0771/5310/aafd8.png)
![P = \frac{( 110 sin [2 \pi * 60t])^2}{ 144}](/tpl/images/0771/5310/aad64.png)
![P = \frac{ 110^2 [ sin [120 \pi t])^2}{ 144}](/tpl/images/0771/5310/9d8b9.png)
![U = \int\limits^T_0 { \frac{ 110^2* [sin [120 \pi t])^2}{ 144}} \, dt](/tpl/images/0771/5310/ca0b8.png)
![U = \frac{110^2}{144} \int\limits^T_0 { ( sin^2 [120 \pi t]} \, dt](/tpl/images/0771/5310/c9738.png)
![U = \frac{110^2}{144} [\frac{t}{2} - [\frac{1}{2} * \frac{sin(240 \pi t)}{240 \pi} ] ]\left | T} \atop {0}} \right.](/tpl/images/0771/5310/203e7.png)
![U = \frac{110^2}{144} [\frac{t}{2} - [\frac{1}{2} * \frac{sin(240 \pi t)}{240 \pi} ] ]\left | 18000} \atop {0}} \right.](/tpl/images/0771/5310/18433.png)
![U = \frac{110^2}{144} [\frac{18000}{2} - [\frac{1}{2} * \frac{sin(240 \pi (18000))}{240 \pi} ] ]](/tpl/images/0771/5310/3f943.png)
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A 100-W (watt) light bulb has resistance R=143Ω (ohms) when attached to household current, where vol...
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