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A 120 V fish-tank heater is rated at 130W. Calculate (a) the current through the heater when it is operating, and (b) its resistance

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Trancescient

Explanation:

The power P dissipated by a heater is defined as

[tex]P = VI[/tex]

where V is the voltage and I is the current.

a) The current running through a 130-W heater is

[tex]I = \dfrac{P}{V} = \dfrac{130\:\text{W}}{120\:\text{V}} = 1.08\:\text{A}[/tex]

b) The resistance R of the heater is

[tex]P = VI = (IR)I = I^2R[/tex]

where [tex]V= IR[/tex] is our familiar Ohm's Law.

[tex]\Rightarrow R = \dfrac{P}{I^2} = \dfrac{130\:\text{W}}{(1.08\:\text{A})^2}[/tex]

[tex]R = 110.8\:Ω[/tex]

The current running through the heater when it is operating is 1.08 A.

The resistance of the heater is 110.8 ohm.

What is current?

  • A current is a flow of Charges.
  • The formula of current is , current I = power P / voltage V
  • The SI unit of current is ampere A.

So, from the above equation we can calculate,

              current I = P/V

                      ∴   I = 130 / 120

                      ∴   I = 1.08 A

What is resistance?

  • The resistance is a quantity which oppose the current flow in a circuit.
  • The formula of resistance is ( in the terms of power P and ohm's law V=IR )  resistance R = P/I^2.
  • The SI unit of resistance is ohm.

So, from the equation we can calculate,

                   Resistance R = P/I^2

                                  ∴  R = 130/(1.08)^2

                                  ∴  R = 110.8 ohm

Thus, the current running through the heater when it is operating is 1.08 A.

The resistance of the heater is 110.8 ohm.

Learn more about resistance and resistivity here -

https://brainly.com/question/13735984

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