Question

An electric tea kettle has two heating coils. When one of the coils is switched on, the kettle begins to boil in 6 minutes. When the other is switched on, the boiling begins in 8 minutes. In what time will boiling begin if both coils are switched on simultaneously (i) in series and (ii) in parallel?

Answer 1

Both kettles dissipate the same energy. The difference is in their resistances.\[\dfrac{V^2}{R_1}\cdot 6 = \dfrac{V^2}{R_2}\cdot 8\]\[R_2 = \dfrac{8}{6}R_1\]

Answer 2

\[E = \dfrac{V^2}{R_1} \cdot 6 \Rightarrow \dfrac{ER_1}{V^2} =6\]\[E = \dfrac{V^2}{R_{\rm eff}}t\]\[E= \dfrac{V^2}{\frac{14}{6}R_1}t\]\[\dfrac{14}{6}\dfrac{ER_1}{V_2} = t \Rightarrow t = 14 \]

Answer 3

If the resistance is \(R_1\), it takes 6 minutes.
If the resistance is \(14/6 \cdot R_1\), it takes 14 minutes because \(E \propto \frac{1}{R}\) and \(E \propto t\).

Answer 4

Or\[E \propto \dfrac{t}{R}\]Or\[t \propto RE\]

Answer 5

Nice.