A circuit consists of resistors R1, R2, R3, R4, R5 with values R1 = 20 Ohm, R2 = 20 Ohm, R3 = 50 Ohm, R4 = 15 Ohm, R5 = 10 Ohm. The voltage across points A and B is UAB = 100 V. Calculate the total resistance R and the total current I.

Analysis of the circuit:

• Resistors R1 and R2 are connected in series.
• Resistor R3 is connected in parallel with the series combination of R1 and R2.
• Resistors R4 and R5 are connected in series.
• The parallel combination of (R1, R2) and R3 is connected in series with the parallel combination of R4 and R5.

Calculations:

1. Resistance of R1 and R2 in series (R12):

   \[ R_{12} = R_1 + R_2 = 20 \text{ Ом} + 20 \text{ Ом} = 40 \text{ Ом} \]

2. Resistance of the parallel combination of R12 and R3 (R123):

   \[ R_{123} = \frac{R_{12} \times R_3}{R_{12} + R_3} = \frac{40 \text{ Ом} \times 50 \text{ Ом}}{40 \text{ Ом} + 50 \text{ Ом}} = \frac{2000}{90} \text{ Ом} \approx 22.22 \text{ Ом} \]

3. Resistance of R4 and R5 in series (R45):

   \[ R_{45} = R_4 + R_5 = 15 \text{ Ом} + 10 \text{ Ом} = 25 \text{ Ом} \]

4. Total resistance (R): This is the series combination of R123 and R45.

   \[ R = R_{123} + R_{45} \approx 22.22 \text{ Ом} + 25 \text{ Ом} \approx 47.22 \text{ Ом} \]

5. Total current (I): Using Ohm's Law (I = U/R)

   \[ I = \frac{U_{AB}}{R} = \frac{100 \text{ В}}{47.22 \text{ Ом}} \approx 2.12 \text{ А} \]

Ответ:

• R = 47.22 Ом
• I = 2.12 А