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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 |
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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 Ω
`R_2 = V_2/I_2 = 5/11.25` = 0.44 Ω
`R_3 = V_3/I_3 = 6/13.5` = 0.44 Ω
| V (Volt) | I (Ampere) | R(Ω) = `bb(V/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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