A series LR circuit contains an emf source of having no internal resistance, a resistor, a inductor having no appreciable resistance, and a switch. If the emf across the inductor is of its maximum value after the switch is closed, what is the resistance of the resistor

b. 1.9 Ω

Explanation:

Here is the complete question

A series LR circuit contains an emf source of 14 V having no internal resistance, a resistor, a 34 H inductor having no appreciable resistance, and a switch. If the emf across the inductor is 80% of its maximum value 4.0 s after the switch is closed, what is the resistance of the resistor? a. 1.5 ? b. 1.9 ? c. 5.0 ? d. 14 ?

Solution

The voltage across the inductor V is

where V₀ = emf of source = 14 V, R = resistance, L = inductance = 34 H and t = time

Given that V = 80% of its maximum value after 4.0 s, this implies that V = 80 % of V₀ = 0.8V₀ and t = 4.0 s

Since and V = 0.8V₀.

Since we need to find R, we make R subject of the formula, we have

taking natural logarithm of both sides, we have

㏑(V/V₀) = -Rt/L

R = -L㏑(V/V₀)/t

Substituting the values of the variables into the equation, we have

R = -34㏑(0.8V₀/V₀)/4.0 s

R = -34㏑(0.8)/4.0 s

R = -34 × -0.2231/4.0 s

R = 7.587/4

R = 1.896 Ω

R ≅ 1.9 Ω

So, B is the answer

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.

an electric circuit