Figure 1 shows a section of an electrical circuit. Perform the necessary calculations and fill in the table. The table contains columns for conductor 1, conductor 2, conductor 3, and the entire circuit section. Rows are for current (I, A), voltage (U, B), and resistance (R, Ohm). Given resistances are: R1 = 3 Ohm, R2 = 30 Ohm, R3 = 30 Ohm. The total voltage across the circuit section is 1 V.

Question

Вопрос:

Figure 1 shows a section of an electrical circuit. Perform the necessary calculations and fill in the table. The table contains columns for conductor 1, conductor 2, conductor 3, and the entire circuit section. Rows are for current (I, A), voltage (U, B), and resistance (R, Ohm). Given resistances are: R1 = 3 Ohm, R2 = 30 Ohm, R3 = 30 Ohm. The total voltage across the circuit section is 1 V.

Ответ:

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Accepted Answer

Analysis of the circuit:

The image displays a circuit diagram with three resistors labeled 1, 2, and 3. Resistors 2 and 3 are connected in parallel, and this parallel combination is then connected in series with resistor 1. The total voltage across the entire circuit section is given as 1 V.

We are given the following resistances:

Resistor 1 ($$R_1$$): 3 Ohm
Resistor 2 ($$R_2$$): 30 Ohm
Resistor 3 ($$R_3$$): 30 Ohm

We need to calculate the current ($$I$$) and voltage ($$U$$) for each resistor and for the entire circuit section.

Step 1: Calculate the equivalent resistance of the parallel combination of R2 and R3.

The formula for two resistors in parallel is:

$$ R_{23} = \frac{R_2 \times R_3}{R_2 + R_3} $$

Substituting the given values:

$$ R_{23} = \frac{30 \text{ Ohm} \times 30 \text{ Ohm}}{30 \text{ Ohm} + 30 \text{ Ohm}} = \frac{900 \text{ Ohm}^2}{60 \text{ Ohm}} = 15 \text{ Ohm} $$

Step 2: Calculate the total equivalent resistance of the circuit.

Resistor 1 is in series with the parallel combination of R2 and R3 ($$R_{23}$$). So, the total resistance ($$R_{total}$$) is:

$$ R_{total} = R_1 + R_{23} $$

$$ R_{total} = 3 \text{ Ohm} + 15 \text{ Ohm} = 18 \text{ Ohm} $$

Step 3: Calculate the total current flowing through the circuit.

Using Ohm's Law ($$I = U / R$$) for the entire circuit section:

$$ I_{total} = \frac{U_{total}}{R_{total}} $$

$$ I_{total} = \frac{1 \text{ V}}{18 \text{ Ohm}} \approx 0.0556 \text{ A} $$

This total current flows through Resistor 1.

Step 4: Calculate the voltage drop across Resistor 1.

$$ U_1 = I_{total} \times R_1 $$

$$ U_1 = \frac{1}{18} \text{ A} \times 3 \text{ Ohm} = \frac{3}{18} \text{ V} = \frac{1}{6} \text{ V} \approx 0.1667 \text{ V} $$

Step 5: Calculate the voltage drop across the parallel combination of R2 and R3.

This is the total voltage minus the voltage drop across R1:

$$ U_{23} = U_{total} - U_1 $$

$$ U_{23} = 1 \text{ V} - \frac{1}{6} \text{ V} = \frac{5}{6} \text{ V} \approx 0.8333 \text{ V} $$

Alternatively, using Ohm's Law for the parallel combination:

$$ U_{23} = I_{total} \times R_{23} $$

$$ U_{23} = \frac{1}{18} \text{ A} \times 15 \text{ Ohm} = \frac{15}{18} \text{ V} = \frac{5}{6} \text{ V} \approx 0.8333 \text{ V} $$

This voltage ($$U_{23}$$) is across both R2 and R3.

Step 6: Calculate the current flowing through Resistor 2 and Resistor 3.

For Resistor 2:

$$ I_2 = \frac{U_{23}}{R_2} $$

$$ I_2 = \frac{5/6 \text{ V}}{30 \text{ Ohm}} = \frac{5}{180} \text{ A} = \frac{1}{36} \text{ A} \approx 0.0278 \text{ A} $$

For Resistor 3:

$$ I_3 = \frac{U_{23}}{R_3} $$

$$ I_3 = \frac{5/6 \text{ V}}{30 \text{ Ohm}} = \frac{5}{180} \text{ A} = \frac{1}{36} \text{ A} \approx 0.0278 \text{ A} $$

Verification: The sum of currents $$I_2$$ and $$I_3$$ should equal the total current flowing into the parallel branch ($$I_{total}$$ that flows through R1, which is $$I_{total} = rac{1}{18} ext{ A}$$).

$$ I_2 + I_3 = \frac{1}{36} \text{ A} + \frac{1}{36} \text{ A} = \frac{2}{36} \text{ A} = \frac{1}{18} \text{ A} $$

This matches $$I_{total}$$.

Summary of results for the table:

Current (I, A):

Conductor 1 ($$I_1$$): $$rac{1}{18}$$ A (or approx. 0.0556 A)
Conductor 2 ($$I_2$$): $$rac{1}{36}$$ A (or approx. 0.0278 A)
Conductor 3 ($$I_3$$): $$rac{1}{36}$$ A (or approx. 0.0278 A)
Entire circuit section ($$I_{total}$$): $$rac{1}{18}$$ A (or approx. 0.0556 A)

Voltage (U, V):

Conductor 1 ($$U_1$$): $$rac{1}{6}$$ V (or approx. 0.1667 V)
Conductor 2 ($$U_2$$): $$rac{5}{6}$$ V (or approx. 0.8333 V)
Conductor 3 ($$U_3$$): $$rac{5}{6}$$ V (or approx. 0.8333 V)
Entire circuit section ($$U_{total}$$): 1 V

Resistance (R, Ohm):

Conductor 1 ($$R_1$$): 3 Ohm
Conductor 2 ($$R_2$$): 30 Ohm
Conductor 3 ($$R_3$$): 30 Ohm
Entire circuit section ($$R_{total}$$): 18 Ohm

Filled table:

	1 проводник	2 проводник	3 проводник	На всём участке цепи
I, A	1/18 (≈0.056)	1/36 (≈0.028)	1/36 (≈0.028)	1/18 (≈0.056)
U, B	1/6 (≈0.167)	5/6 (≈0.833)	5/6 (≈0.833)	1
R, Ом	3	30	30	18

Ответ: Заполненная таблица представлена выше.