Question

Электродвижущая сила батарейки для карманного фонаря 4,5 В. При внешнем сопротивлении 12 Ом ток в цепи равен 0,3 А. Определить внутреннее сопротивление батарейки и ток короткого замыкания.

Answer 1

I=E/(R+r)

I(R+r)=E

Ir+IR=E

Ir=E-IR

r=(E-IR)/ I

I=0.3

R=12

E=4.5

r=(4.5-0.3*12) / 0.3=3 Ом

 

Ток короткого замыкания

I=E/r

I=4.5/3=1.5 А

Answer 2

Calculation of Internal Resistance and Short Circuit Current

To determine the internal resistance of the battery and the short circuit current, we can use Ohm's law and the concept of voltage division.

Given: - Electromotive force (EMF) of the battery (ε): 4.5 V - External resistance (R): 12 Ω - Current in the circuit (I): 0.3 A

We can use Ohm's law to calculate the internal resistance (r) of the battery:

Ohm's Law: V = I * R

The voltage across the external resistance (V_R) can be calculated as the product of the current (I) and the resistance (R):

V_R = I * R

The voltage across the internal resistance (V_r) can be calculated as the difference between the EMF (ε) and the voltage across the external resistance (V_R):

V_r = ε - V_R

Since the internal resistance (r) is in series with the external resistance (R), the total current (I) can be calculated as the ratio of the voltage across the external resistance (V_R) to the total resistance (R + r):

I = V_R / (R + r)

To find the short circuit current (I_short), we can assume that the external resistance (R) is zero:

I_short = ε / r

Now let's calculate the internal resistance (r) and the short circuit current (I_short) using the given values:

1. Calculate the voltage across the external resistance (V_R): - V_R = I * R - V_R = 0.3 A * 12 Ω - V_R = 3.6 V

2. Calculate the voltage across the internal resistance (V_r): - V_r = ε - V_R - V_r = 4.5 V - 3.6 V - V_r = 0.9 V

3. Calculate the internal resistance (r): - I = V_R / (R + r) - 0.3 A = 3.6 V / (12 Ω + r) - 0.3 A * (12 Ω + r) = 3.6 V - 3.6 Ω + 0.3 A * r = 3.6 V - 0.3 A * r = 3.6 V - 3.6 Ω - 0.3 A * r = 0 V - r = 0 Ω

4. Calculate the short circuit current (I_short): - I_short = ε / r - I_short = 4.5 V / 0 Ω - I_short = ∞ (infinity)

Results:

Based on the calculations, the internal resistance of the battery is 0 Ω and the short circuit current is ∞ (infinity).

Please note that the result of zero internal resistance and infinite short circuit current may not be physically realistic. This could be due to the limitations of the calculations or the assumptions made. It is important to consider the practical limitations and characteristics of real batteries in such scenarios.