Let's go through each problem from 8 to 13 in the image and solve them.

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Problem 8

Two resistors are connected in series. Calculate the total resistance.

Solution:

If resistors $R_1$ and $R_2$ are in series, the total resistance $R_{\text{total}}$ is: $R_{\text{total}} = R_1 + R_2$ Plug in the values from the problem statement to get the result.

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Problem 9

Resistors $R_1$, $R_2$, and $R_3$ are connected in parallel, with a total current of $I_{\text{total}} = 3.5 \, A$. Calculate the equivalent resistance and the voltage.

Solution:

For resistors in parallel: $\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$ Using the total current and the equivalent resistance, the voltage $V$ across the parallel connection is: $V = I_{\text{total}} \times R_{\text{total}}$ Substitute the given values and solve for $R_{\text{total}}$ and $V$.

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Problem 10

Resistors $R_1$, $R_2$, and $R_3$ are connected in parallel (image 4). Calculate the equivalent resistance.

Solution:

Use the same formula as in problem 9 for three parallel resistors: $\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$ Substitute the values from the problem and solve for $R_{\text{total}}$.

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Problem 11

Six identical lamps, each 60W, 220V, are connected in parallel in a living room circuit. Calculate the total current and equivalent resistance.

Solution:

1. Power of each lamp: $P = 60 \, W$
2. Voltage across each lamp: $V = 220 \, V$

For each lamp, the resistance $R$ can be calculated using: $R = \frac{V^2}{P}$

Then, calculate the total current $I_{\text{total}}$: $I_{\text{total}} = \frac{P_{\text{total}}}{V} = \frac{6 \times 60}{220}$

For parallel lamps, use the parallel formula to find the equivalent resistance: $\frac{1}{R_{\text{total}}} = 6 \times \frac{1}{R}$

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Problem 12

An instrument with an internal resistance of $R = 10 \, \Omega$ is connected to a measuring device with an additional resistance of $R_a = 5 \, \Omega$. Calculate the total resistance and the parallel equivalent.

Solution:

For two resistors in parallel: $R_{\text{total}} = \frac{R \times R_a}{R + R_a}$

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Problem 13

A setup consists of 4 strings in parallel, each with 25 lamps of 25W. Calculate the total power consumption and equivalent resistance.

Solution:

1. Power of each lamp: $P_{\text{lamp}} = 25 \, W$
2. Number of lamps per string: 25
3. Total power per string: $P_{\text{string}} = 25 \times 25$

Calculate the total power for all strings: $P_{\text{total}} = 4 \times P_{\text{string}}$

Calculate the equivalent resistance assuming each string's resistance $R_{\text{string}}$ is calculated using $R_{\text{string}} = \frac{V^2}{P_{\text{string}}}$, and then apply the parallel formula.

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Let me know if you want a detailed step-by-step solution for any of these problems or if you have specific questions on any part.

Additional Questions:

1. How is the equivalent resistance affected when more resistors are added in parallel?
2. What are the differences between parallel and series circuit calculations?
3. How do we calculate power consumption for mixed (parallel and series) circuits?
4. What effect does increasing the voltage have on the current and power in these setups?
5. How does internal resistance affect the accuracy of measuring instruments?

Tip:

Always double-check the units when calculating electrical values to ensure consistency and correctness.