Question

The electric capacitance of biological tissues serves as the basis for numerous medical technologies. For example, dielectric spectroscopy glucose reading (DSGR) is a noninvasive diagnostic technique that uses the electric capacitance of blood to estimate blood glucose levels.

A DSGR device records the electric current that results from applying a voltage source to the skin and underlying blood vessels. DSGR can be modeled by the circuit shown in Figure 1, in which V represents the applied potential, C_B represents the capacitance of the blood, and R_E, R_D, and R_B represent the electrical resistances of the epidermis, the dermis, and the blood, respectively.

Figure 1 DSGR circuit model including skin and superficial blood vessel

The capacitance of charged blood may be explained by red blood cell membranes acting as physical barriers that separate electrons introduced into the blood from positively charged ions in the red blood cell cytoplasm. The dielectric constant k of red blood cell membranes varies with glucose concentration (Figure 2) because glucose uptake by red blood cells alters the activity of membrane-bound proteins that regulate the flow of ions into and out of the cell.

Figure 2 Blood dielectric constant vs blood glucose concentration

DSGR readings vary with blood glucose concentration because the time needed to fully charge the blood is related to total blood capacitance. However, interpreting DSGR readings may be complicated by changes in biological variables other than blood capacitance. For example, the resistivity of blood varies in accordance with osmolarity such that changes in diet or hydration status influence the current measured by DSGR devices.

Biological system Circuit model 1.4 DSGR Electrodes Epidermis x1.3 RE Rp Dermis O 1.0 0.9 Blood 2.5 7.5 10 12.5 15 17.5 20 CB Glucose concentration (mM)

Which of the following statements best describes the behavior of the circuit in Figure 1 when the fully charged capacitor (comprising red blood cells) is discharged?

1. The electric currents through R_B and R_E are equal because the resistors are in series.
2. The voltage drops across R_B and R_E are equal because the resistors are in parallel.
3. The electric currents through R_B exceeds that through R_E because the capacitor is fully charged.
4. Both the current and voltage drops across R_B and R_E are equal because the same power source is used.    

Answer 1

Correct statement is (B).

Here resistance R_B and R_E are in parallel with battery and the capacitor.

so when we apply kirchoff’s loop law then potential drop across each resistance is equal and its value is V.

Now, current through resistance is given by : i = V/R

so current through R_B = i_B = V/R_B

current through R_E = i_E = V/R_E

potential drop is same but current is different.