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Find the resistance of human body?

Problem 1:  A person touches live wire of a 100 watt closed circuit. If supply voltage is 200 volt and total current flow in a circuit (when touches) is 0.55 ampere, then find the resistance of the human body?

Solution: The circuit shown in diagram is similar to a parallel resistive circuit. We are interested to find the resistance of human body. In order to make this problem easy, let’s draw a resistive circuit of given diagram.

Here, R_B  is resistance of bulb_.
R_H  is Resistance of human body.

As R_B  and R_H are connected in parallel, so 0.55 current will divided into two parts. Total current of the circuit is current flow through R_B and R_H.
In order to find current through bulb, first we have to calculate its resistance (R_B).
Power (P)  =   V²/R_B
             R_B =   V²/P
R_B =  (200 x 200) / 100
             R_B = 400 Ω

Hence, current through bulb (I_B)
                I_B = V/R
                I_B = 200/400
I_B = 0.5 Amp.

As total current flow through circuit is 0.55 and current flow through bulb is 0.5 Ampere. Therefore, current flow through human body (I_H) is
          I_H = 0.55 – 0.5
          I_H = 0.05 Amp.

The voltage across human body is 200 volt. Hence resistance of human body (R_H) is equal to
              R_H = V/I    (because, V = IR)
R_H = 200 / 0.05
R_H = 4000 Ω
In short, Resistance of human body is 4000 ohms. 

Problem 2:  A person touches live wire of a closed circuit. The supply voltage is 220 volt and total current flow in a circuit (when touches) is 0.60 ampere. If the current flow through bulb is 0.50 then find the resistance of the human body?

Solution: This problem is almost similar to above one. It is more easier to solve. Let us consider R_B  is resistance of bulb and R_H  is Resistance of human body.

Given in the question,
Total circuit current (I) = 0.6 Amp
Current flow through bulb (I_B) = 0.5 Amp
Supply Voltage (V) = 220 V

As we discussed in problem 1, R_B  and R_H are connected in parallel, so 0.55 current will divided into two parts. Total current of the circuit is current flow through R_B and R_H.

i.e       Total current (I) = I_B  +    I_H
Therefore,
current flow through human body (I_H) is
          I_H = 0.6 – 0.5
          I_H = 0.1 Amp.

The voltage across human body is 220 volt. Hence resistance of human body (R_H) is equal to
R_H = V/I    (because, V = IR)
R_H = 220/ 0.1
R_H = 2200 Ω
In short, Resistance of human body is 2200 ohms.