Q.A galvanic cell has electrical potential of $1.1\ V$. If an opposing potential of $1.1\ V$ is applied to this cell, what will happen to the cell reaction and current flowing through the cell?

The key idea is that the cell reaction proceeds spontaneously only when the applied opposing potential is less than the cell’s EMF. Here, the applied potential exactly equals the cell potential.

Step 1: The cell’s EMF is $1.1\ \text{V}$, meaning the spontaneous reaction drives electrons with this driving force.

Step 2: Applying an exactly equal opposing potential ($1.1\ \text{V}$) cancels this driving force — the net potential difference becomes zero. …

The key here is understanding what happens when you “fight” a galvanic cell with an external voltage. A galvanic cell spontaneously produces electricity because its two half-cells have different reduction potentials — electrons flow from the anode to the cathode through the external circuit. The cell’s electromotive force (EMF), here $1.1\ \text{V}$, is the driving force for that spontaneous reaction.

Now, if you connect an external power source in opposition — positive to positive, negative to negative — you are essentially trying to push electrons back the other way. This is exactly how electrolysis works: when the applied voltage exceeds the cell’s EMF, you force the reverse reaction. But here the applied voltage is exactly equal to the cell’s EMF, not greater.

Let’s walk through what that means.

1. The Nernst equation tells us the cell potential depends on concentrations. For a Daniell cell (the classic $1.1\ \text{V}$ example: $\text{Zn}|\text{Zn}^{2+}||\text{Cu}^{2+}|\text{Cu}$), the cell reaction is

The Nernst equation at $298\ \text{K}$ is

where $Q = \frac{[\text{Zn}^{2+}]}{[\text{Cu}^{2+}]}$ and $n=2$. Under standard conditions ($1\ \text{M}$ each), $E_{\text{cell}} = 1.1\ \text{V}$.

2. When you apply an opposing voltage exactly equal to $E_{\text{cell}}$, the net driving force becomes zero. Think of it like two people pulling a rope with exactly equal force in opposite directions — nothing moves. The external power supply exactly cancels the cell’s tendency to push electrons. Mathematically, the net potential difference across the external circuit is

With zero net voltage, no electrons are driven through the circuit.

3. No current flows — the cell is at equilibrium.

   Current requires a potential difference. Since $E_{\text{net}} = 0$, the current $I = 0$. The cell reaction stops because there is no longer any driving force for electron transfer. The system is now at dynamic equilibrium: the forward and reverse rates are equal, but macroscopically, no net reaction occurs.

4. What about the concentrations? …

Method: Electrochemical Cell Equilibrium Analysis (using Nernst Equation & Overpotential Concept)

Step 1: Understand the given condition

• Cell potential ($E_{cell}$) = $1.1\ V$ (spontaneous, positive)
• Applied opposing potential = $1.1\ V$ (exactly equal and opposite)

Step 2: Compare applied potential with cell potential

When an external voltage is applied opposite to the cell's direction:

• If applied $E < E_{cell}$ → cell still discharges (but slower)
• If applied $E = E_{cell}$ → no net reaction (equilibrium)
• If applied $E > E_{cell}$ → cell reaction reverses (electrolysis)

Here, applied $E = E_{cell}$, so the system is at equilibrium.

Step 3: Apply the Nernst equation logic

At equilibrium:

The Nernst equation:

When $E_{cell} = E_{applied}$, the reaction quotient $Q$ equals the equilibrium constant $K$.

Thus, no net reaction occurs — the forward and backward rates are equal.

Step 4: Determine current flow …

Here are the common mistakes students make when solving this type of question, along with how to avoid each.

Mistake 1: Thinking the cell reaction stops completely

Why it happens

Students assume that when applied voltage equals cell potential ($E_{\text{cell}} = E_{\text{applied}}$), the reaction simply "stops." They forget that at this point, the cell is at equilibrium — the reaction is still occurring in both directions at equal rates.

How to avoid

Remember:

• If $E_{\text{applied}} < E_{\text{cell}}$ → cell works normally (spontaneous reaction).
• If $E_{\text{applied}} = E_{\text{cell}}$ → no net reaction, but dynamic equilibrium exists.
• If $E_{\text{applied}} > E_{\text{cell}}$ → electrolysis (reverse reaction).

So here, with $E_{\text{applied}} = 1.1\ \text{V} = E_{\text{cell}}$, the net cell reaction stops, but the system is at equilibrium.

Mistake 2: Saying current becomes zero immediately

Why it happens

Students think "no net reaction" means zero current instantly. In reality, at the exact balancing potential, current approaches zero only after equilibrium is reached.

How to avoid

Use the Nernst equation logic:

At equilibrium, $Q = K$ and $E_{\text{cell}} = 0$ (for a cell at equilibrium). But here, the applied voltage exactly cancels the cell's driving force — so no net electron flow occurs. Current becomes zero (or negligible) because there is no net driving force.

Mistake 3: Confusing this with electrolysis

Why it happens

Students see "opposing potential" and immediately think of electrolytic cells. They forget that equal opposing potential does not reverse the reaction — it only stops it.

How to avoid

• Opposing potential < cell potential → cell still discharges (but slower).
• Opposing potential = cell potential → no net reaction (equilibrium).
• Opposing potential > cell potential → electrolysis (reverse reaction starts).

Here, $1.1\ \text{V}$ exactly equals the cell potential, so no electrolysis occurs.

Mistake 4: Forgetting to mention "no net reaction" vs "reaction stops"

Why it happens …