Question

In a recording of voltages due to brain activity (an EEG), a 10.0 mVsignal with an 0.500Hz frequency is applied to a capacitor, producing a current of 100mA. Resistance is negligible. (a) What is the capacitance? (b) What is unreasonable about this result? (c) Which assumption or premise is responsible?

Short answer

a) The capacitance is 3.18 F .

b) The capacitance is too high.

c) The voltage is too low.

Step-by-step solution

Definition of Inductance and Reactance

Inductance: The property of an electric conductor that causes an electromotive force to be generated owing to a change in current flow is known as inductance.

Reactance: The inertia against the motion of electrons in an electrical circuit, or the property against the flow of electrons in an electrical circuit, is referred to as reactance.

Given data

Voltage due to brain activity (an EEG), is $V=10.0mV\left(\frac{{10}^{-3}V}{1mV}\right)=1.00\times {10}^{-2}V$a

The frequency of the signal is $f=0.50Hz$

The produced current is$l=100mA\left(\frac{{10}^{-3}A}{1mA}\right)=0.100A$

Calculating capacitance(a)

The formula to calculate the capacitance can be expressed as,

$X_C=\left(\frac{1}{2\pi fC}\right)$…………(1)

Here $X_C$is the capacitive reactance, f the frequency, and C the inductance.

Further, we can write the current in terms of,

$l=\frac{V}{X_C}$……………..(2)

Using equation (2) in equation (1), we can write,

$C=\frac{l}{2\pi fV}$…………(3)

Substituting the given values in the above equation (3), we get,

$$\begin{gathered} C=\frac{0.100A}{2\times 3.14\times 0.500Hz\times 1.00\times {10}^{-2}V} \\ =3.18F \end{gathered}$$

Therefore, the capacitance is $C=3.18F$.

Explanation of unreasonable result in part (a)(b)

Consider the calculated capacitance,

That's a huge amount of capacity. A capacitance of 3.18 F could easily fill a huge room.

Therefore, the result is a massive capacitance.

Step 5: Assumption or premise which is responsible(c)

It is implausible to believe that such a low voltage could produce such a current at such a low frequency. At low frequencies, capacitive resistance is quite high unless the capacitance is very large.

Hence, at low frequencies, capacitive resistance is quite high unless the capacitance is very large.