Question

В сеть с напряжением 220 В параллельно включены две группы ламп. В одной группе восемь ламп с сопротивление 160 Ом каждая, а в другой десять ламп с сопротивление 200 Ом каждая. Определить полное сопротивление и общую силу тока.

Answer 1

$R_{1-10} = R_{1} + R_{2} +...+R_{10}$

$R_{1-10} = 2000$ Ом

$R_{11-19} = R_{11} + R_{12} +...+R_{19}$

$R_{11-19} = 1280$ Ом

$\frac{1}{R} = \frac{1}{R_{1-10}} + \frac{1}{R_{11-19}}$

$\frac{1}{R} = \frac{1}{2000} + \frac{1}{1280}$

$\frac{1}{R} = \frac{41}{32000}$

$R = \frac{32000}{41} = 780.5$ Ом - общее сопротивление

Answer 2

Calculation of Total Resistance and Total Current

To determine the total resistance and total current in the parallel circuit, we need to calculate the equivalent resistance and use Ohm's law.

Let's start by calculating the equivalent resistance of the two groups of lamps in parallel.

For the first group with eight lamps, each lamp has a resistance of 160 Ohms. Since the lamps are connected in parallel, the reciprocal of the equivalent resistance is equal to the sum of the reciprocals of the individual resistances:

Equivalent resistance of the first group: 1/R1 = 1/160 + 1/160 + 1/160 + 1/160 + 1/160 + 1/160 + 1/160 + 1/160

Simplifying the equation: 1/R1 = 8/160

R1 = 160/8 = 20 Ohms

For the second group with ten lamps, each lamp has a resistance of 200 Ohms. Again, since the lamps are connected in parallel, we can calculate the equivalent resistance using the same formula:

Equivalent resistance of the second group: 1/R2 = 1/200 + 1/200 + 1/200 + 1/200 + 1/200 + 1/200 + 1/200 + 1/200 + 1/200 + 1/200

Simplifying the equation: 1/R2 = 10/200

R2 = 200/10 = 20 Ohms

Now that we have the equivalent resistance of both groups, we can calculate the total resistance of the circuit by adding the reciprocals of the equivalent resistances:

Total resistance: 1/RTotal = 1/R1 + 1/R2

Simplifying the equation: 1/RTotal = 1/20 + 1/20

1/RTotal = 2/20

RTotal = 20/2 = 10 Ohms

To find the total current, we can use Ohm's law:

Total current: I = V / RTotal

Given that the voltage is 220 V, we can substitute the values into the equation:

I = 220 / 10

I = 22 Amperes

Therefore, the total resistance of the circuit is 10 Ohms, and the total current flowing through the circuit is 22 Amperes.

Please note that the calculations provided are based on the given information and assumptions.