A charge of #40 C# passes through a circuit every #8 s#. If the circuit can generate #16 W# of power, what is the circuit's resistance?

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Answer 1 · 2016-09-11T13:32:19

#R = 0.64# Ω

One of the formulas for electric power is #P = I^(2) R#.

Also, electric current is defined as the flow of charge.

Mathematically, this is expressed as #I = (Q) / (t)#.

Let's substitute this expression of #I# into the equation for electric power:

#=> P = ((Q) / (t))^(2) R#

#=> P = (Q^(2)) / (t^(2)) R#

Then, let's rearrange the equation to express it in terms of #R#:

#=> R = ((P t^(2)) / (Q^(2)))# Ω

Now, let's substitute the values for electric charge, time and electric power:

#=> R = ((16 cdot 8^(2)) / (40^(2)))# Ω

#=> R = ((16 cdot 64) / (1600))# Ω

#=> R = ((1024) / (1600)) # Ω

#=> R = 0.64# Ω