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The heating coil of a geyser draws a current of \[7.5{\text{ A}}\] when connected to a source maintaining a potential difference of \[200{\text{ V}}\] between its terminals. What is the resistance of the coil?

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Last updated date: 13th Jul 2024
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Answer
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Hint: The resistance in an electric circuit can be calculated by applying Ohm’s law to it. Ohm’s law states that the amount of current flowing through an electric circuit is directly proportional to the voltage applied across the circuit. is a proportionality constant and is defined as the resistance applied to the flow of current in the circuit by the conductor. It's S.I. unit is Ohm, \[\Omega \]. The current flowing through the circuit is thus inversely proportional to the resistance.

 Formula used:
The Ohm’s Law is given by,
\[\begin{gathered}
  V\alpha I \\
  V = IR \\
\end{gathered} \]
\[I\]is the current passing through the circuit, \[V\]is the voltage applied across the circuit, \[R\]is the resistance.

Complete step by step answer:
The Ohm’s Law is given by,
\[V\alpha I\]
\[ \Rightarrow V = IR\]
\[I\] is the current passing through the circuit, \[V\]is the voltage applied across the circuit, \[R\]is the resistance.
\[R\]is a proportionality constant and is defined as the resistance applied to the flow of current in the circuit by the conductor. It's S.I. unit is Ohm, \[\Omega \]. The current flowing through the circuit is thus inversely proportional to the resistance.
Substitute \[7.5{\text{ A}}\]for \[I\] and \[200{\text{ V}}\] for \[V\]in equation (1) as
\[200{\text{ V}} = \left( {7.5{\text{ A}}} \right)R\]
\[ \Rightarrow R = \dfrac{{200{\text{ V}}}}{{7.5{\text{ A}}}}\]
\[ \Rightarrow R = 26.67{\text{ }}\Omega \]

Therefore, the resistance of the coil is \[26.67{\text{ }}\Omega \].

Note: Ohm’s law studies the current and voltage in an electric circuit and their impact on the various properties of the electrical elements present in the circuit. Most of the electrical devices obey Ohm’s law and are called Ohmic devices. However, Ohm’s law is valid only when the parameters like temperature and other physical conditions remain constant. Ohm’s law forms the basic law of any electrical analysis as it gives us the values of current, voltage, and resistance which further helps us in calculating the power consumed by a circuit. Ohm’s law does not apply to unilateral and non-linear electrical devices like diodes, transistors, capacitors, etc.