Question

The coil of resistance \[10\Omega \] and an inductance \[5H\] is connected to a \[100V\] battery. The energy stored in the coil is,
A. \[125erg\]
B. \[125J\]
C. \[250erg\]
D. \[250J\]

Answer 1

Hint: In an electrical circuit, Ohm's Law is a formula for calculating the relationship between voltage, current, and resistance. If you know the voltage and current and want to know resistance means we can use ohm’s law formula. So if we use the ohm's law we can easily find the answer.

Formula used:
\[V = IR\]
\[V\] - Voltage
\[I\] - current
\[R\] - Proportionality constant, or resistance

Formula used:
The ohm's law states that,
\[I = \dfrac{V}{R}\]
Where, \[V = 100V\]
\[R = 10 ohm\]
\[I = \dfrac{{100}}{{10}} = 10A\]
The energy stored in the coil is given as,
\[U = \dfrac{{L{I^2}}}{2}\]
\[L\] - Inductance
\[I\] - Current
\[U = \dfrac{{5 \times {{(10)}^2}}}{2} = 250J\]
Hence option (D) is correct.

Note:
Since resistance cannot be measured in an operational circuit, Ohm's Law comes in handy when calculating it. Instead of shutting down the circuit to test resistance, a technician can use the above variant of Ohm's Law to figure out R. The static values of circuit components, current levels, voltage supplies, and voltage dips can all be validated using Ohm's Law.