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This is one of our many quizzes on Ohm's law. Click on this to access more such competitive quizzes on Current Electricity and EMI.

Ohm's law Quiz 2

physics

 Resistance of a copper wire with a length of $5\text{ }m$ and the area of cross section $5\text{ }{{m}^{2}}$ has been mentioned as $65\text{ }\Omega $.  The current passing through the wire has been mentioned as $32.5\text{ }A$. What will be the electric field produced there? 

The ohm’s law says that the voltage will be proportional to the current in the circuit. The electric field will be the ratio of the potential to the length of the copper wire.  

 The voltage can be found by the equation,$  V=IR $ $\\ $ Substituting the values in the equation will give, $ \\ V=32.5\times 65 \\  \Rightarrow V=2112.5\text{ }V \\ $ The electric can be found by the equation given as, $ \\ E=\dfrac{V}{l} \\  \Rightarrow E=\dfrac{2112.5}{5} \\  \therefore E=422.5\text{ }V{{m}^{-1}}$ 

The current flowing through a wire has been mentioned as $3\text{ }A$ when Mohit did an experiment. The voltmeter is showing a reading of $24\text{ }V$. Calculate the resistance of the wire. 

 The resistance of the wire can be found by the ratio of the voltage to the current flowing in the circuit. 

 Here the resistance can be found by the equation given as,$ \\ R=\dfrac{V}{I}\\ $ Substituting the values in the equation will give, $ \\  R=\dfrac{24}{3} \\ \therefore R=8\text{ }\Omega$ 

 Vibha and Neha did the same experiment using the identical wire in all sense. But Vibha got the value of resistance as $3.5\text{ }\Omega $ and Neha got the value as $35\text{ }\Omega $. What will be the percentage error in both of their calculations respectively if the original value of the resistance is $350\text{ }\Omega $? 

The percentage error will be the ratio of the difference of original resistance to the observed resistance to the original resistance. This is to be multiplied by a hundred. 

 The percentage error in resistance can be found by the equation, $ \\ $ $\% \text{ error}=\dfrac{\text{Original resistance-Observed resistance}}{\text{Original resistance}} \times 100\\ $ The percentage error of the resistance observed by Vibha will be, $\\ $ $ \% \text{ error=}\dfrac{350-3.5}{350} \times 100\\  \Rightarrow\text{ % error=}99\% \\ $ The percentage error in resistance observed by Neha will be, $\\ \% \text{ error=}\dfrac{350-35}{350}\times 100 \\  \therefore \%\text{ error=}90\% $

If a material of length $10\text{ }m$ and the area $100\text{ }{{m}^{2}}$ is having a resistance of $5\text{ }\Omega $, what will be the conductance of the material? 

The conductance can be found by taking the reciprocal of the value of resistance. Its unit is given as Siemens.  

The conductance will be the reciprocal of the resistance. That is we can write that, $ \\  R=\dfrac{1}{\sigma } \\  \Rightarrow \sigma =\dfrac{1}{R} \\ $ Substituting the values in the equation will give, $ \\ \sigma =\dfrac{1}{5} \\  \therefore \sigma =0.2\text{ siemens}$ 

 Vini is confused about the unit of conductivity. Elsa told her that the unit of conductivity is Siemens. Is she correct? 

Conductivity can be found by taking the ratio of the product of length of the wire and the conductance to the area of the wire.

 The unit, Siemens mentioned is not the unit of conductivity. It is the unit of conductance.Conductivity can be found by taking the reciprocal of the resistivity. The unit of conductivity will be Siemens per metre.