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Question
The following table shows the current in Amperes and potential differences in Volts.
- Find the average resistance.
- What will be the nature of the graph between the current and potential difference? (Do not draw a graph.)
- Which law will the graph prove? Explain the law.
| V (volts) | I (amp) |
| 4 | 9 |
| 5 | 11.25 |
| 6 | 13.5 |
Solution
From the following table,
V1 = 4V, V2 = 5V, V3 = 6V
I1 = 9 A, I2 = 11.25 A, I3 = 13.5 A
`"R"_1 = "V"_1/"I"_1 = 4/9 = 0.44 Omega`
`"R"_2 = "V"_2/"I"_2 = 5/11.25 = 0.44 Omega`
`"R"_3 = "V"_3/"I"_3 = 6/13.5 = 0.44 Omega`
| V (Volt) | I (Ampere) | R(Ω) = `bb"V"/bb"I"` |
| 4 | 9 | 0.44 |
| 5 | 11.25 | 0.44 |
| 6 | 13.5 | 0.44 |
a. Average resistance (R) = `("R"_1 + "R"_2 + "R"_3)/3`
= `(0.44 + 0.44 + 0.44)/3`
= `1.32/3 = 0.44`
∴ Average resistance (R) = 0.44 Ω
b. A straight line will pass through the origin (0, 0) on the graph between current and potential difference.
c. Here `"V"_1/"I"_1 = "V"_2/"I"_2 = "V"_3/"I"_3` i.e. Ohm's law is clear from I ∝ V.
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