People who work with electronics are often heard to say that something is “grounded.” It always sounds quite serious, perhaps somewhat mysterious. What is it?

The circuit analysis procedures we have discussed so far deal only with potential differences. Although we are free to choose the zero point of potential anywhere that is convenient, our analysis of circuits has not revealed any need to establish a zero point. Potential differences are all we have needed.

Difficulties can begin to arise, however, if you want to connect two different circuits together. Perhaps you would like to connect your DVD to your television or your computer monitor to the computer itself. Incompatibilities can arise unless all the circuits to be connected have a common reference point for the potential.

You learned previously that the earth itself is a conductor. Suppose we have two circuits. If we connect one point of each circuit to the earth by an ideal wire, and we also agree to call the potential of the earth $V_{\text{earth}}=0\text{V}$, then both circuits have a common reference point. But notice something very important: one wire connects the circuit to the earth, but there is not a second wire returning to the circuit. That is, the wire connecting the circuit to the earth is not part of a complete circuit, so there is no current in this wire! Because the wire is an equipotential, it gives one point in the circuit the same potential as the earth, but it does not in any way change how the circuit functions. A circuit connected to the earth in this way is said to be grounded, and the wire is called the ground wire.

FIGURE 28.32a shows a fairly simple circuit with a 10 V battery and two resistors in series. The symbol beneath the circuit is the ground symbol. It indicates that a wire has been connected between the negative battery terminal and the earth, but the presence of the ground wire does not affect the circuit’s behavior. The total resistance is $8\text{Ω}+12\text{Ω}=20\text{Ω}$, so the current in the loop is $I=(10\text{V})\text{/}\left(20\text{Ω}\right)=0.50\text{A}$. The potential differences across the two resistors are found, using Ohm’s law, to be $\text{Δ}{V}_8=4\text{V}$ and $\text{Δ}{V}_{12}=6\text{V}$. These are the same values that we would find if the ground wire were not present. So what has grounding the circuit accomplished?

FIGURE 28.32 A circuit that is grounded at one point.

Full Alternative Text

FIGURE 28.32b shows the actual potential at several points in the circuit. By definition, $V_{\text{earth}}=0\text{V}$. The negative battery terminal and the bottom of the $12\text{Ω}$ resistor are connected by ideal wires to the earth, so the potential at these two points must also be zero. The positive terminal of the battery is 10 V more positive than the negative terminal, so $V_{\text{neg}}=0\text{V}$ implies $V_{\text{pos}}=+10\text{V}$. Similarly, the fact that the potential decreases by 6 V as charge flows through the $12\text{Ω}$ resistor now implies that the potential at the junction of the resistors must be $+6\text{V}$. The potential difference across the $8\text{Ω}$ resistor is 4 V, so the top has to be at $+10\text{V}$. This agrees with the potential at the positive battery terminal, as it must because these two points are connected by an ideal wire.

All that grounding the circuit does is allow us to have specific values for the potential at each point in the circuit. Now we can say “The voltage at the resistor junction is 6 V,” whereas before all we could say was “There is a 6 V potential difference across the $12\text{Ω}$ resistor.”

There is one important lesson from this: Being grounded does not affect the circuit’s behavior under normal conditions. You cannot use “because it is grounded” to explain anything about a circuit’s behavior.

We added “under normal conditions” because there is one exception. Most circuits are enclosed in a case of some sort that is held away from the circuit with insulators. Sometimes a circuit breaks or malfunctions in such a way that the case comes into electrical contact with the circuit. If the circuit uses high voltage, or even ordinary 120 V household voltage, anyone touching the case could be injured or killed by electrocution. To prevent this, many appliances or electrical instruments have the case itself grounded. Grounding ensures that the potential of the case will always remain at 0 V and be safe. If a malfunction occurs that connects the case to the circuit, a large current will pass through the ground wire to the earth and cause a fuse to blow. This is the only time the ground wire would ever have a current, and it is not a normal operation of the circuit.

EXAMPLE 28.11 A grounded circuit

Suppose the circuit of Figure 28.32 were grounded at the junction between the two resistors instead of at the bottom. Find the potential at each corner of the circuit.

VISUALIZE FIGURE 28.33 shows the new circuit. (It is customary to draw the ground symbol so that its “point” is always down.)

FIGURE 28.33 Circuit of Figure 28.32 grounded at the point between the resistors.

FIGURE 28.33 Full Alternative Text

SOLVE Changing the ground point does not affect the circuit’s behavior. The current is still 0.50 A, and the potential differences across the two resistors are still 4 V and 6 V. All that has happened is that we have moved the $V=0\text{V}$ reference point. Because the earth has $V_{\text{earth}}=0\text{V}$, the junction itself now has a potential of 0 V. The potential decreases by 4 V as charge flows through the $8\text{Ω}$ resistor. Because it ends at 0 V, the potential at the top of the $8\text{Ω}$ resistor must be $+4\text{V}$. Similarly, the potential decreases by 6 V through the $12\text{Ω}$ resistor. Because it starts at 0 V, the bottom of the $12\text{Ω}$ resistor must be at $-6\text{V}$. The negative battery terminal is at the same potential as the bottom of the $12\text{Ω}$ resistor, because they are connected by a wire, so $V_{\text{neg}}=-6\text{V}$. Finally, the potential increases by 10 V as the charge flows through the battery, so $V_{\text{pos}}=+4\text{V}$, in agreement, as it should be, with the potential at the top of the $8\text{Ω}$ resistor.

REVIEW A negative voltage means only that the potential at that point is less than the potential at some other point that we chose to call $V=0\text{V}$. Only potential differences are physically meaningful, and only potential differences enter into Ohm’s law: $I=\text{Δ}V\text{/}R$. The potential difference across the $12\text{Ω}$ resistor in this example is 6 V, decreasing from top to bottom, regardless of which point we choose to call $V=0\text{V}$.