Question

1. plot a graph of current versus voltage for voltage values ranging from 10 v to 100 v in 10 v steps for each of the following resistance values: (a) 1.0ω (b) 5.0ω (c) 20ω (d) 100ω

Answer:

To solve the problem of plotting current vs. voltage for different resistances, we use Ohm's Law (\(I = \frac{V}{R}\)) to calculate current for each voltage and resistance.

Part (a): Resistance \(R = 1.0\,\Omega\)

Step 1: List Voltage Values

Voltage values: \(10\,\text{V}, 20\,\text{V}, 30\,\text{V}, 40\,\text{V}, 50\,\text{V}, 60\,\text{V}, 70\,\text{V}, 80\,\text{V}, 90\,\text{V}, 100\,\text{V}\)

Step 2: Calculate Current for Each Voltage

Using \(I = \frac{V}{R}\) with \(R = 1.0\,\Omega\):

• For \(V = 10\,\text{V}\): \(I = \frac{10}{1.0} = 10\,\text{A}\)
• For \(V = 20\,\text{V}\): \(I = \frac{20}{1.0} = 20\,\text{A}\)
• For \(V = 30\,\text{V}\): \(I = \frac{30}{1.0} = 30\,\text{A}\)
• For \(V = 40\,\text{V}\): \(I = \frac{40}{1.0} = 40\,\text{A}\)
• For \(V = 50\,\text{V}\): \(I = \frac{50}{1.0} = 50\,\text{A}\)
• For \(V = 60\,\text{V}\): \(I = \frac{60}{1.0} = 60\,\text{A}\)
• For \(V = 70\,\text{V}\): \(I = \frac{70}{1.0} = 70\,\text{A}\)
• For \(V = 80\,\text{V}\): \(I = \frac{80}{1.0} = 80\,\text{A}\)
• For \(V = 90\,\text{V}\): \(I = \frac{90}{1.0} = 90\,\text{A}\)
• For \(V = 100\,\text{V}\): \(I = \frac{100}{1.0} = 100\,\text{A}\)

Part (b): Resistance \(R = 5.0\,\Omega\)

Step 1: Use Ohm's Law

Using \(I = \frac{V}{R}\) with \(R = 5.0\,\Omega\):

• For \(V = 10\,\text{V}\): \(I = \frac{10}{5.0} = 2\,\text{A}\)
• For \(V = 20\,\text{V}\): \(I = \frac{20}{5.0} = 4\,\text{A}\)
• For \(V = 30\,\text{V}\): \(I = \frac{30}{5.0} = 6\,\text{A}\)
• For \(V = 40\,\text{V}\): \(I = \frac{40}{5.0} = 8\,\text{A}\)
• For \(V = 50\,\text{V}\): \(I = \frac{50}{5.0} = 10\,\text{A}\)
• For \(V = 60\,\text{V}\): \(I = \frac{60}{5.0} = 12\,\text{A}\)
• For \(V = 70\,\text{V}\): \(I = \frac{70}{5.0} = 14\,\text{A}\)
• For \(V = 80\,\text{V}\): \(I = \frac{80}{5.0} = 16\,\text{A}\)
• For \(V = 90\,\text{V}\): \(I = \frac{90}{5.0} = 18\,\text{A}\)
• For \(V = 100\,\text{V}\): \(I = \frac{100}{5.0} = 20\,\text{A}\)

Part (c): Resistance \(R = 20\,\Omega\)

Step 1: Apply Ohm's Law

Using \(I = \frac{V}{R}\) with \(R = 20\,\Omega\):

• For \(V = 10\,\text{V}\): \(I = \frac{10}{20} = 0.5\,\text{A}\)
• For \(V = 20\,\text{V}\): \(I = \frac{20}{20} = 1\,\text{A}\)
• For \(V = 30\,\text{V}\): \(I = \frac{30}{20} = 1.5\,\text{A}\)
• For \(V = 40\,\text{V}\): \(I = \frac{40}{20} = 2\,\text{A}\)
• For \(V = 50\,\text{V}\): \(I = \frac{50}{20} = 2.5\,\text{A}\)
• For \(V = 60\,\text{V}\): \(I = \frac{60}{20} = 3\,\text{A}\)
• For \(V = 70\,\text{V}\): \(I = \frac{70}{20} = 3.5\,\text{A}\)
• For \(V = 80\,\text{V}\): \(I = \frac{80}{20} = 4\,\text{A}\)
• For \(V = 90\,\text{V}\): \(I = \frac{90}{20} = 4.5\,\text{A}\)
• For \(V = 100\,\text{V}\): \(I = \frac{100}{20} = 5\,\text{A}\)

Part (d): Resistance \(R = 100\,\Omega\)

Step 1: Use Ohm's Law

Using \(I = \frac{V}{R}\) with \(R = 100\,\Omega\):

• For \(V = 10\,\text{V}\): \(I = \frac{10}{100} = 0.1\,\text{A}\)
• For \(V = 20\,\text{V}\): \(I = \frac{20}{100} = 0.2\,\text{A}\)
• For \(V = 30\,\text{V}\): \(I = \frac{30}{100} = 0.3\,\text{A}\)
• For \(V = 40\,\text{V}\): \(I = \frac{40}{100} = 0.4\,\text{A}\)
• For \(V = 50\,\text{V}\): \(I = \frac{50}{100} = 0.5\,\text{A}\)
• For \(V = 60\,\text{V}\): \(I = \frac{60}{100} = 0.6\,\text{A}\)
• For \(V = 70\,\text{V}\): \(I = \frac{70}{100} = 0.7\,\text{A}\)
• For \(V = 80\,\text{V}\): \(I = \frac{80}{100} = 0.8\,\text{A}\)
• For \(V = 90\,\text{V}\): \(I = \frac{90}{100} = 0.9\,\text{A}\)
• For \(V = 100\,\text{V}\): \(I = \frac{100}{100} = 1\,\text{A}\)

Plotting the Graph

For each resistance, plot voltage (x-axis) vs. current (y-axis). The data points for each resistance are as calculated above. The graphs will be straight lines passing through the origin (since \(I \propto V\) for a fixed resistance, Ohm's Law), with slopes \(\frac{1}{R}\) (steeper for smaller resistances).

Final Answer (Data for Plotting)

• (a) \(1.0\,\Omega\):

\(V\) (V): 10, 20, 30, 40, 50, 60, 70, 80, 90, 100
\(I\) (A): 10, 20, 30, 40, 50, 60, 70, 80, 90, 100

• (b) \(5.0\,\Omega\):

\(V\) (V): 10, 20, 30, 40, 50, 60, 70, 80, 90, 100
\(I\) (A): 2, 4, 6, 8, 10, 12, 14, 16, 18, 20

• (c) \(20\,\Omega\):

\(V\) (V): 10, 20, 30, 40, 50, 60, 70, 80, 90, 100
\(I\) (A): 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5

• (d) \(100\,\Omega\):

\(V\) (V): 10, 20, 30, 40, 50, 60, 70, 80, 90, 100
\(I\) (A): 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1

To plot, use these coordinates and draw straight lines through the origin for each resistance.