The current flowing into a certain circuit is monitored carefully over time. All voltages quoted assume the positive reference terminal is the top of the two circuit terminals. I is observed that for the first two hours, a current of 1mA flows into the top terminal, while a voltage of +5V is measured. Over the next 30 minutes, no current flows in or out. The, for two hours, a current of 1mA flows out of the top terminal, with a voltage of +2V measured. After that, no current flows in or out again. Assuming the circuit had no energy initially stored, answer the following:

a) How much power was delivered to the circuit during of the three intervals?

b) How much energy was supplied to the circuit during the first two hours of observation?

c) How much energy remains in the circuit now

Passo 1

a) Para calcular as potências, basta aplicar os valores das correntes e tensões em cada intervalo na fórmula da potência:

P p r i m e i r a s   2   h o r a s = 5 V × 0.001 A = 5   m W

P p r ó x i m o s   30   m i n u t o s = 5 V × 0 A = 0   W

P ú l t i m a s   2   h o r a s = 2 V × - 0.001 A = - 2   m W

Passo 2

b) Para calcularmos a energia fornecida ao circuito durante as duas primeiras horas, temos que lembrar que a potência é a taxa de variação da energia a cada segundo, logo para obtermos a energia, basta multiplicar a potência fornecida ao circuito naquele período pelo período(de 2 horas convertido para segundos):

E = 5 × 10 - 3 × 2 × 60 × 60 = 36   J  

Passo 3

c) A energia restante no circuito vai ser a diferença entre a energia recebida nas primeira duas horas pela energia gasta nas últimas duas horas:

36 J - 2 × 0.001 × 60 × 60   J = 21.6   J

Resposta

a )   P p r i m e i r a s   2   h o r a s = 5   m W

P p r ó x i m o s   30   m i n u t o s = 0   W

P ú l t i m a s   2   h o r a s = - 2   m W

b) 36   J

c) 21.6   J