No electric current will flow between two charged bodies if both bodies have the same value of which of the following physical quantities?

Introduction / Context:
This question addresses a core concept in basic electricity: the driving cause of electric current between two points. Current flows when there is a potential difference, similar to how water flows when there is a difference in water level. Understanding that equal potentials imply no net driving force for charge flow is essential for students learning about circuits, capacitors and electrostatics. Many general knowledge and entrance exam questions test whether learners correctly identify electric potential, not just charge, as the deciding factor.

Given Data / Assumptions:

• Two bodies are charged and may have different or equal charges.
• Electric current will flow only if there is some driving difference between them.
• The options include resistance, charge, potential and charge to potential ratio.
• We assume that the bodies can be connected by a conductor that allows charge to move.

Concept / Approach:
Electric potential (or electric potential energy per unit charge) at a point determines how much work is done in bringing a small test charge from a reference point to that point. When two conductors are at different potentials and connected by a path for charge, charges will flow from higher potential to lower potential until the potentials become equal. The actual amount of charge each body carries is not decisive; what matters is the difference in potential. Electric resistance determines how much current flows for a given potential difference but does not by itself cause current when the potential difference is zero. Therefore, if two bodies have the same potential, no current will flow between them when they are connected.

Step-by-Step Solution:
Step 1: Recall Ohm law in basic form: I = V / R, where I is current, V is potential difference and R is resistance. Step 2: Notice that if V, the potential difference, is zero, then I becomes zero regardless of the value of R, meaning no current flows. Step 3: Understand that two bodies can have different amounts of charge yet be at the same potential, especially when their shapes or sizes differ. Step 4: Recognise that equal potential implies equal electric potential energy per unit charge, so there is no net driving force pushing charges from one body to the other. Step 5: Conclude that no current flows when the electric potentials of the two bodies are equal, making potential the correct quantity in the question.

Verification / Alternative check:
A helpful check is to think about charging two identical metal spheres. If both are brought to the same potential using a voltage source and then connected with a wire, no spark is observed and no current flows because there is no potential difference. On the other hand, if they have different potentials and are then connected, a transient current flows until their potentials equalise. This practical behaviour confirms that equal potential, not equal charge or equal resistance, is the condition for no current flow between the bodies.

Why Other Options Are Wrong:
Equal electrical resistance does not prevent current; current depends on both resistance and potential difference. Two resistors with equal resistance can still have current flowing through them if connected to a voltage source. Equal charge on both bodies does not guarantee zero potential difference, because potential also depends on size, shape and environment. Equal charge to potential ratio is not a standard criterion used in electrostatics, and in any case the flow is determined directly by potential difference, not by this ratio.

Common Pitfalls:
A common mistake is to think that if two bodies carry the same amount of charge, there is no tendency for charge to move between them. However, if their capacities differ, they may still be at different potentials, and current can flow. Another confusion arises when students focus on resistance and overlook the crucial role of potential difference. To avoid such errors, always remember that electric current flows due to potential difference, and if potentials are equal, current cannot flow between the bodies through a conductor.

Final Answer:
No current will flow between two charged bodies if they have the same electric potential.