Capacitance Current and Power

In summary, the conversation discusses finding the current, power, and energy stored over time for a capacitor with a value of 0.01 Farads and a voltage of v(t) = 100*cos(2pi60t). The equations for current (i(t)), power (p(t)), and energy (w) are provided, and the attempt at a solution involves determining the current to be -120*pi*sin(2pi60t) Amperes. However, this does not match the given answer of -18,850sin(2pi120t) Watts. The suggestion is made to use a trig identity for Sin(2X) to clarify the discrepancy.
  • #1
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Homework Statement



The voltage across a capacitor with a value of 0.01 Farads is v(t) 100*cos(2pi60t). Find i(t),p(t),and w(t).


Homework Equations



i(t)=Cv'(t) [current]
p(t)=i(t)v(t) [power]
w= integral of p(t) [Energy stored over time]

The Attempt at a Solution



I was able to correctly determine the current of capacitance, -120*pi*sin(2pi60t) Amperes. However, this multiplied by the voltage, does NOT equal the given answer of -18,850sin(2pi120t) Watts.

Could someone please clear this up for me? I would've used proper symbols, but the test is quite shortly, no time to mess with that ... :/

Thanks!
 
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  • #2
Try using a trig identity for Sin(2X).
 

1. What is capacitance?

Capacitance is the ability of a capacitor to store electric charge. It is measured in Farads (F) and is represented by the symbol C.

2. What is current?

Current is the flow of electric charge through a circuit. It is measured in Amperes (A) and is represented by the symbol I.

3. How is capacitance related to current?

Capacitance and current are inversely related. This means that as the capacitance of a capacitor increases, the current decreases, and vice versa.

4. What is power in relation to capacitance and current?

Power is the rate at which energy is transferred or converted. In the context of capacitance and current, power is the product of voltage and current, represented by the equation P=VI.

5. How can capacitance, current, and power be calculated?

Capacitance can be calculated using the formula C=Q/V, where Q is the charge and V is the voltage. Current can be calculated using the formula I=Q/t, where t is the time. Power can be calculated using the formula P=VI. These calculations can also be done using a circuit simulator or a multimeter.

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