Question

Doua becuri au aceeasi tensiune nominala si puterile nominale P1= 40W, respectiv P2= 60W. In ce raport se vor afla puterile consumate la conectarea celor doua becuri in serie?

Answer 1

Răspuns:

$P_{1} = \frac{U_{n}^{2} }{R_{1} } \\P_{2} = \frac{U_{n}^{2} }{R_{2} } \\=> \frac{P_{1}}{P_{2}} = \frac{U_{n}^{2} }{R_{1} } \frac{R_{2} }{ U_{n}^{2}} =\frac{R_{2}}{R_{1}}$

⇒ $\frac{R_{1}}{R_{2}}=\frac{P_{2}}{P_{1}}$

La conectarea celor doua becuri in serie, becurile sunt stabatute de acelai curent electric, $I_{s}$

$P'_{1} = I_{s}^{2}R_{1}\\P'_{2} = I_{s}^{2}R_{2}\\\frac{P'_{1}}{P'_{2}} = \frac{ I_{s}^{2}R_{1}}{I_{s}^{2}R_{2}} = \frac{R_{1}}{R_{2}}$

dar  $\frac{R_{1}}{R_{2}}=\frac{P_{2}}{P_{1}}$

⇒ $\frac{P'_{1}}{P'_{2}} =\frac{P_{2}}{P_{1}} = \frac{60}{40} = \frac{3}{2}$

⇒ $\frac{P'_{1}}{P'_{2}} = \frac{3}{2}$