Shunts: Using wire & a DMM to measure current Richard Perez Use the wire that's already in your system to make current measurements. All you need is a tape measure, a meter, and the information right here. It's easy and will answer the perennial question, "How much does it draw, anyway?" In Theory Ohm's law informs us that any electrical current flowing through a material (like a piece of wire) suffers a loss in voltage. This voltage drop across the material is due to its resistance and the movement of the electrons (current) through that material. The amount of current flowing through the material can be determined if we know two things. One, the voltage loss across the material, and Two, the resistance of the material. Or in algebraic terms using Ohm's Law: I=E/R (Equation1) where I= the amount of current in Amperes E= the voltage drop in Volts R= the material's resistance in Ohms Well, every appliance, power converter, power source and whatever is wired into the system with copper wire. The wiring in necessary to move electrical current from place to place, from source to load, etc. If we consider these bits of wire as resistors, then we can use the amount of voltage loss across a wire to determine the amount of current flowing through the wire. Wire used in such a fashion is called a "shunt" in electronics jargon. How it Works All we need to perform current measurements on our PV panels, inverters, refrigerators, or any other device that consumes, stores, produces, or converts electricity is a Digital MultiMeter (DMM) and the already existing wire in our systems. And a little help from Ohm's Law. The DMM is used to measure the voltage drop across a piece of wire carrying current. The DMM should be capable of making measurements in the millivolt DC range. For example, the Fluke 77 we use at Home Power can measure down to 000.1 millivolts (mV or thousandths of a Volt). Such resolution is necessary as this technique involves using lengths of wire with resistances from 0.1½ to 0.0001½. The resultant voltage drops across such small resistances will be very low, and we'll need a DMM that can make accurate measurements in the milliVolt range. At about $140, the Fluke is a good deal for a 0.03% accuracy, very rugged, DMM. Radio Shack also offers DMMs that will measure in the mV. range for around $60. We also need to know, as accurately as possible, the resistance of the piece of copper wire we are using. To find this resistance first determine the wire's size or gauge. Most wire has its gauge number printed on its insulation. Or the wire's gauge can be determined by using a wire gauge measuring tool. Once the gauge number is known, then measure the length of the wire. Copper wire has its resistance, in Ohms per foot, specified by gauge number. Once we know the gauge, we can look up the resistance (½/ft) in the Copper Wire Table (See BasicElectric ¥ Home Power #2). This value is multiplied by the number of feet of wire we are using to make the measurement. And the result is the resistance of that particular piece of copper wire or shunt. This technique can be used on wire of any size, and of any length. There are certain resistance values for shunts that have distinct advantages. Consider the following resistances: 0.1½, 0.01½, 0.001½, and 0.0001½. If these values are used for R in Equation 1, then we are performing division by a decimal fraction of 1. This means that the measurement taken by the DMM can be read directly and a calculator is not needed to perform the math. Only the decimal point of the reading of the DMM need be shifted to obtain the amperage measurement. What follows below is a Copper Wire Table that is optimized to display the lengths of various gauges that have resistances from 0.1½ to 0.0001½. Find the wire gauge size of the wire you are using, and the lengths necessary to produce the shunts are shown across the table. Measure the indicated length along your wire and you have a shunt with a resistance that is a decimal fraction of 1. Attach the leads of the DMM across this length and you're ready to make current measurements. At the head of each shunt column on the table, there is a reminder to shift the decimal point on the mV. reading taken from the DMM. For example, let's consider a 12 VDC light hooked up with 12 gauge wire. From the shunt table, we see that 0.63 feet of this 12 gauge wire will give us a shunt of 0.001½. The heading of the column tells us that the milliVolt (mV.) reading on the meter will equal the amperes of current through the shunt. If we measure 4.2 mV. across this 0.001½ shunt, then the current flowing the shunt (and the light) the light is 4.2 Amperes. If the shunt had a resistance of 0.01 ½ (as in 6.3 feet of 12 ga.), the the milliVolt reading on the DMM would be 42.0 mV. and would have to be divided by 10 to produce the correct amperage measurement of 4.2 Amperes. INSERT COPPER WIRE SHUNT TABLE The schematic shown below shows the electrical setup for using copper wire shunts to measure current. The measurement can be taken in the positive or negative wire, it doesn't make any difference. I've made switch panels to measure current in different place by soldering small (20 gauge) wires to the shunts and running these smaller wires to a panel with a rotary switch. The DMM is connected to the output of the switch which selects the different shunts. The wire need not be cut at the ends of the shunt. Simply strip back the insulation and make the measurement. In places where you don't need to make measurements all the time, use needle probes on the DMM to pierce the insulation without stripping. A piece of string is useful to transfer length measurements from a tape to stiff pieces of nonstraight wire and cable. INSERT SHUNT SCHEMATIC Where to Use Shunts Use this technique any place you wish to measure current. Here are some suggestions. On the main wires delivering current from PV arrays to the batteries. On the wires that supply current to an inverter (this is a great place for a 0.0001½ shunt made out of 2.04 feet of 0000 gauge copper cable). On the wires that connect the battery pack to the bus. And on any appliance whose current consumption needs to be measured. Advantages There are all kinds of advantages in using this technique. The wiring that we are using to make the measurement already exists to move the power to or from the device. The measurement process doesn't introduce any new losses as the shunt wiring is already there. The wiring need not be cut as in the insertion of an in-line meter. Shunts can be made with very low resistances, thus enabling high current measurements with minimum loss. The technique can be used with minimum trouble and no expense for occasional measurements than don't require a dedicated in-line ammeter. Disadvantages The big disadvantage is inaccuracy due to the copper wire changing resistance as it heats or cools. The information on the Copper Wire Shunt Table is correct for copper wire at 68¡F. (20¡C.). For copper wire at 32¡F. (0¡C.), this method will yield amperage measurements that are low by about 10%. At a wire temperature of 122¡F. (50¡C.), this method yields amperage measurements that are high by 10%. If you compensate for the temperature of the wire, this technique can be made more accurate. Nerd Stuff-- Equation City The data on the Shunt Table was calculated from an equation written by the Wizard. While browsing through the Copper Wire Table one afternoon, he noticed this simple exponential relationship between wire gauge size number and the resistance of that sized wire. What follows here is a generalized equation that yields amperage through a shunt of any length and gauge of copper wire. This equation is also compensated for temperature. INSERT EQUATION where: I= current through the copper wire shunt in Amperes (A.) Lm= length of the shunt in meters (m.) mV= voltage drop across the shunt in milliVolts (mV.) Tc= temperature of the shunt wire in degrees Centigrade (¡C.) N= the wire gauge size number (B&S American Standard). Note: use the following integers for these gauge sizes: for 0000 use -3, for 000 use -2, for 00 use -1, and for 0 use 0. In all other cases use the wire gauge number directly. This equation works for gauge numbers between 0000 and 40, even fractional gauges.