The quantities EMF and potential difference have the same units (Volts). Explain

Question

The quantities EMF and potential difference have the same units (Volts). Explain the difference between these two quantities. Briefly describe Ohm's law. What is meant by the term "non-Ohmic." Consider three circuits A (a battery in series with a single resistor), B (a battery in series with two resistors) and C (a battery and two resistors all in parallel with each other) and complete the table below for one of the resistors. In column A the resistor R has a current of i, a voltage drop of V across it, and power P. All the resistors are the same for all circuits and each circuit is connected to a battery of potential V. The first column has been filled out for you. (eg. if the current through R in circuit B was twice that of circuit A, then you would write 2i)

Explanation / Answer

1 a)
Potential difference is the work done to move a unit charge from the negative and positive terminals of a battery.
EMF is the total voltage generated in an electrical circuit by the battery.
EMF = Ir + IR
r is the internal resistance of the battery, IR is the potential difference.
For a new battery, both EMF and potential difference will be almost same. But as time goes on, internal resistance will increase and the potential difference will decrease.

b)
According to Ohm's law, the potential difference between an ideal conductor is proportional to the current though it.
V is proportional to I
V = RI

c)
If we take the slop of voltage and current for an ohmic resistor/conductor,
R = V/I = constant. (we get a straight line)
Anything that doesn't follow this relation is called non-ohmic.
For example, Consider that when current is going through a resistor, its temperature increases. This will further increase/decrease the resistance and we won't get a linear relation between V and I.

2.
Circuit A
i = V/R
P = potential difference x Current = V i

In circuit B,
Total resistance = R + R = 2R
Current = V/2R = 1/2 (V/R) = 0.5 i
Voltage across a single resistor = V/2
Power = V/2 x 0.5 i = P/4

In circuit C,
Total resistance = R x R / (R + R) = R/2
Current = V/ (R/2) = 2 (V/R) = 2 i
Since the connection is parallel, both resistors have the same potential difference, V
Power = V x 2 i = 2 (V i) = 2 P

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