Two identical cells each having an EMF of 1.5V and internal resistance [tex]$0.5 \Omega$[/tex] are connected in series to a coil of resistance [tex]$5 \Omega$[/tex]. What is

a) the effective EMF of the cells?
b) the effective resistance in the circuit?
c) the current in the circuit?
d) the potential difference across the solution resistor?

Solution:



Answer :

Sure, let's solve this problem step-by-step.

We have two identical cells each with an electromotive force (emf) of [tex]\(1.5 \text{ V}\)[/tex] and an internal resistance of [tex]\(0.5 \Omega\)[/tex]. These cells are connected in series to a coil with a resistance of [tex]\(5 \Omega\)[/tex]. We need to determine:

a) The effective emf of the cells in series.
b) The effective resistance in the circuit.
c) The current in the circuit.
d) The voltage drop across the solution resistor (coil).

### a) Effective EMF of the cells in series:

When cells are connected in series, their emf adds up. Therefore, the total emf ([tex]\(E_{total}\)[/tex]) is:

[tex]\[ E_{total} = 1.5 \text{ V} + 1.5 \text{ V} = 3.0 \text{ V} \][/tex]

### b) Effective resistance in the circuit:

The total internal resistance ([tex]\(r_{total}\)[/tex]) of the two cells in series is the sum of their individual resistances:

[tex]\[ r_{total} = 0.5 \Omega + 0.5 \Omega = 1.0 \Omega \][/tex]

Now, the total resistance ([tex]\(R_{total}\)[/tex]) in the circuit is the sum of the total internal resistance of the cells and the resistance of the coil:

[tex]\[ R_{total} = r_{total} + \text{resistance of the coil} \][/tex]
[tex]\[ R_{total} = 1.0 \Omega + 5 \Omega = 6.0 \Omega \][/tex]

### c) Current in the circuit:

Using Ohm's Law, the current ([tex]\(I\)[/tex]) in the circuit is given by:

[tex]\[ I = \frac{E_{total}}{R_{total}} \][/tex]
[tex]\[ I = \frac{3.0 \text{ V}}{6.0 \Omega} = 0.5 \text{ A} \][/tex]

### d) Voltage drop across the coil:

The voltage drop across the coil ([tex]\(V_{coil}\)[/tex]) can be found using Ohm's Law again:

[tex]\[ V_{coil} = I \times \text{resistance of the coil} \][/tex]
[tex]\[ V_{coil} = 0.5 \text{ A} \times 5 \Omega = 2.5 \text{ V} \][/tex]

### Summary:
a) Effective emf of the cells in series: [tex]\(3.0 \text{ V}\)[/tex]

b) Effective resistance in the circuit: [tex]\(6.0 \Omega\)[/tex]

c) Current in the circuit: [tex]\(0.5 \text{ A}\)[/tex]

d) Voltage drop across the coil: [tex]\(2.5 \text{ V}\)[/tex]