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I want to test my setup with 200Ah battery and check the outputs on oscilloscope. While testing can I connect battery ground to the oscilloscope ground?

Is there any safety risk, as oscilloscope internally connected to earth? If I connect to battery's negative terminal, it will be connected to earth. Will it cause any hazard? Battery is of 12 V.

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you are right, you oscilloscope gnd is connected to earth.

You battery can modeled basically by a floating voltage source of 12V. Because it is floating, you can connect its minus terminal to the gnd of the oscilloscope.

At the positive terminal of the battery you will get a voltage that is 12V greater than your oscilloscope gnd. If now you want to measure that 12V with your oscilloscope probe, make sure that 12V is not greater than the max input voltage of the probe. This is generally not an issues if you use standard 10x,1Mohm probes.

But pay attention if you plan to connect to the oscilloscope directly using a BNC connector for instance. The Inputs of my Lecroy accept max 5V and are 50 ohm...

Imagine 12V in 50 ohm :

$$ P = \frac{U^2}R $$

$$ P = \frac{12^2}{50} = 2.88W $$

2.88W the be dissipated by the input of the scope...

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    \$\begingroup\$ That's a very atypical scope input (early digital sampler?), most scope input jacks are rated to a few hundred volts and a 1 megaohm, though may have a 50 ohm termination that can be switched in. Obviously one needs to understand the particular instrument being used in any given case. Also, while line-powered scopes are designed to be grounded to earth through their power cords, and one needs to always assume that they could be one shouldn't assume without verification that they actually are. \$\endgroup\$ Jan 3 '13 at 15:22
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Most likely you'll be fine. A battery is isolated from the mains earth ground. Shorting them will simply set the battery earth and main earth as the same reference.

The only issue will be if the battery ground is somehow otherwise referenced to a potential that's not mains earth isolated.

For example if you have 2 batteries in series and one battery's ground is connected to mains earth, you need to be careful about which battery ground you connect your probe ground to.

You can also use a differential probe. These probes measure the differential voltage between the two test leads, there's not low impedance path from either lead to mains earth.

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