Question

Four cells, each of e.m.f. 2 V and internal resistance 0.2 Ω each are connected in series to form a battery. This battery is connected to an ammeter, a resistance 1.2 Ω and then to a set of resistance of 4 Ω, 6 Ω and 12 Ω in parallel to complete the overall circuit in series.

1. Draw circuit diagram of arrangement.
2. Calculate total internal resistance.
3. Total e.m.f.
4. Current recorded by ammeter.
5. Current flowing through 6 Ω wire in parallel.
6. Drop in potential across the terminals of the battery.

Answer 1

(a)

(b) Internal resistance of 4 cells in series \[=4 \times 0.2\] \[=0.8\text{ Ω}\]

(c) e.m.f. of 4 cells in series \[=4 \times 2\] \[=8\text{ V}\]

(d) Equivalent resistance of 4 Ω, 6 Ω and 12 Ω in parallel \[\frac{1}{R_p}=\frac{1}{4}+\frac{1}{6}+\frac{1}{12}\] \[=\frac{3+2+1}{12}\] \[=\frac{1}{2}\] \[\therefore R_p=2\text{ Ω}\]

Total external resistance \[=1.2+2\] \[=3.2\text{ Ω}\]

Current recorded by ammeter \[I=\frac{E}{R+r}\] \[=\frac{8}{3.2+0.8}\] \[=2\text{ A}\]

(e) p.d. across parallel circuit \[V=IR=2 \times 2\] \[=4\text{ V}\]

Current flowing through 6 Ω resistor \[I=\frac{V}{R}\] \[=\frac{4}{6}\] \[=0.67\text{ A}\]

(f) Drop in potential across the terminals of the battery \[E-V=Ir=2 \times 0.8\] \[=1.6\text{ V}\]