Question

Как и во сколько раз надо изменить силу тока в цепи,чтобы при уменьшении ее сопротивления в 4 раза выделение теплоты в ней осталось прежнем?а)Уменьшить в 2 разаб)Увеличить в 4 разав)Уменьшить в 4 разаг)Увеличить в 2 раза

Answer 1

Q1=(I1)^2R1t    Q2=(I2)^2R2t 
R1=4R2        Q1=Q2 
(I1)^2*4R2t=(I2)^2*R2t      2I1=I2      Т.е. увеличить в 2 раза

Answer 2

The answer is a) Уменьшить в 2 раза. Here is a detailed explanation:

The heat generated in a circuit is proportional to the product of the current and the resistance, according to the formula Q = I^2 * R * t, where Q is the heat, I is the current, R is the resistance, and t is the time. Therefore, if the resistance is reduced by a factor of 4, the current must be reduced by a factor of 2 to keep the heat constant. Mathematically, this can be shown as follows:

Let Q_1 be the initial heat, I_1 be the initial current, and R_1 be the initial resistance. Then, Q_1 = I_1^2 * R_1 * t.

Let Q_2 be the final heat, I_2 be the final current, and R_2 be the final resistance. Then, Q_2 = I_2^2 * R_2 * t.

If the resistance is reduced by a factor of 4, then R_2 = R_1 / 4.

If the heat is unchanged, then Q_2 = Q_1.

Substituting these values into the equations, we get:

Q_1 = I_1^2 * R_1 * t Q_2 = I_2^2 * (R_1 / 4) * t Q_2 = Q_1

Simplifying and canceling out the common terms, we get:

I_2^2 = I_1^2 / 4

Taking the square root of both sides, we get:

I_2 = I_1 / 2

Therefore, the current must be reduced by a factor of 2 to keep the heat constant.

You can find more information about the electric circuits and the laws of Ohm and Kirchhoff from the web search results . I hope this helps.