Question

# A three-way lightbulb can produce 50W, 100W or 150W at120V. Such a bulb contains two filaments that can beconnected to the 120V individually or in parallel. Describehow the connections to the two filaments are made to give each ofthe three wattages. What must be the resistance of eachfilament?

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A three-way lightbulb can produce 50W, 100W or 150W at120V. Such a bulb contains two filaments that can beconnected to the 120V individually or in parallel. Describehow the connections to the two filaments are made to give each ofthe three wattages. What must be the resistance of eachfilament?

2021-05-14
The resistance of the filament
$$\displaystyle{R}=\frac{{V}^{{{2}}}}{{P}}$$
$$\displaystyle{R}_{{{1}}}=\frac{{120}^{{{2}}}}{{50}}={288}\ {o}{h}{m}{s}$$
$$\displaystyle{R}_{{{2}}}=\frac{{120}^{{{2}}}}{{100}}={144}\ {o}{h}{m}{s}$$
$$\displaystyle{R}_{{{3}}}=\frac{{120}^{{{2}}}}{{150}}={96}\ {o}{h}{m}{s}$$
If the filaments are conected in parallel then
$$\displaystyle{R}_{{{1}}}={R}_{{{a}}}+{R}_{{{b}}}$$
$$\displaystyle{R}_{{{a}}}={R}_{{{b}}}={144}\ {o}{h}{m}{s}$$