Don't Touch It!

The secondary side of an AC transformer supplies 240 240 volts rms. A cable with 2 2 ohms of resistance each way connects the transformer to a load resistance of 50 50 ohms. One terminal of the transformer is connected to earth ground, as shown.

Suppose you touch the return terminal on the load, thinking it should be safe. Your body's resistance is 1000 1000 ohms, and your feet are at earth potential. How many milli-amps of current (mA rms) flow through your body?


The answer is 8.87.

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1 solution

Tom Engelsman
Nov 25, 2018

Let V V denote the transformer's voltage and V R V_{R} be the voltage at the Return junction. By applying Kirchhoff's Current Law at the Return junction, one obtains the following relationship:

V R V ( 2 + 50 ) Ω = 0 V R 1000 Ω + 0 V R 2 Ω \frac{V_{R} - V}{(2 + 50) \Omega} = \frac{0 - V_{R}}{1000 \Omega} + \frac{0 - V_{R}}{2 \Omega} ;

or ( 1 52 + 1 1000 + 1 2 ) V R = V 52 = 240 52 (\frac{1}{52} + \frac{1}{1000} + \frac{1}{2})V_{R} = \frac{V}{52} = \frac{240}{52} ;

or V R = 8.872 V_{R} = 8.872 volts. The current running through you (if you dare!) computes to (by Ohm's Law): I = V R 1000 Ω = 8.872 × 1 0 3 I = \frac{V_{R}}{1000 \Omega} = 8.872 \times 10^{-3} , or 8.872 m A . \boxed{8.872 mA}.

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