# Capacitance of a Grounded Capacitor

Suppose one plate of the capacitor is grounded which means there is charge present at only one plate. We know that the potential across the capacitor will be 0, i.e., V=0.

And capacitance of the Capacitor will be C=Q/V

C=Q/0 implying C=∞

So it means that the capacitance of a grounded capacitor is Infinite. I know this is not true as a conductor cannot store infinite electrical energy.

So where am I going wrong?

• No, the fact that one plate is grounded does not mean that there is no charge on that plate. Look up "charging by induction" which leaves a charge on a conductor even though it is grounded. Sep 10 '16 at 14:10
• What is your definition of capacitance if the two plates do not carry same amount of opposite charges? Sep 10 '16 at 14:30
• Well for a Capacitor having unequal charge on its plates I don't know because I haven't read about it yet . If u know please tell me and is there anything of this post related to it? @velut. Please let me know Sep 10 '16 at 15:47
• @sammygerbil charge at one end will induce opposite charge at another end(which is grounded) of the capacitor. If the induced charge is +ve incoming electrons from the ground will neutralize them and in case of -ve charge they will flow to the earth. So I don't think so that there will be any charge on the grounded plate of the capacitor Sep 10 '16 at 15:50

Suppose one plate of the capacitor is grounded which means there is charge present at only one plate.

The electric potential of an ideal ground does not change no matter how much charged is added or removed. From the Wikipedia article Ground (electricity)

In electronic circuit theory, a "ground" is usually idealized as an infinite source or sink for charge, which can absorb an unlimited amount of current without changing its potential.

So, attaching one capacitor plate to ground simply fixes the electric potential of that plate; if the ungrounded plate has charge $Q$, the grounded plate will have charge $-Q$.

how could the grounded plate gain -Q charge.

The ideal ground supplies the $-Q$ charge to the plate without changing potential.

If somehow it gains -Q charge it will flow to the earth.

No, that's not correct. A common problem in electrostatics is calculating the surface charge on a grounded plane when a charge $Q$ is placed some height above the plane. Essentially, the charge flows until the electrostatic energy of the configuration is minimum which, in the case of the grounded plate capacitor, is when there is charge $-Q$ on the grounded plate which is as close to the $Q$ charge as is possible.

OK I got u but why the potential across a grounded capacitor is taken 0

It isn't taken to be zero unless $Q=0$.

• So you mean there will be no change if I connect the negative plate of a capacitor to a conducting sphere with radius of one light year? Sep 10 '16 at 14:57
• @AlfredCentauri how could the grounded plate gain -Q charge. If somehow it gains -Q charge it will flow to the earth. Now if I am wrong then please edit your answer with appropriate detail. Sorry for any inconvenience Sep 10 '16 at 15:53
• Mritun Jay. I suggest you study about grounded bodies in detail. You have a confusion regarding what grounding a plate means. Sep 10 '16 at 17:25
• @MritunJay, the ground supplies the -Q charge to the grounded plate of the capacitor. A common problem in electrostatics is calculating the induced surface charge on a grounded plate when a charge Q is placed some height above it. Similarly, for the grounded plate of a capacitor. See, for example, this Sep 10 '16 at 17:49
• OK I got u but why the potential across a grounded capacitor is taken 0. Are we taking earth as a reference point or something else? Sep 10 '16 at 17:53

Actually, when an uncharged plate is grounded its charge remains always zero. But if a charged plate is brought near to the uncharged plate, a induced potential of the same type developed at the far side of the grounded plate which is neutralized by the ground and thereby developing a net +ve or -ve charge. Thus capacitance never goes infinite.