Question

The figures below show four circuits, with the resistances of the resistors given. In all cases, the emf of the battery is 10 V. Rank the circuits in order of descending total current coming out of the battery. (You should be able to answer this question using what you have already learned, but if you want, feel free to build the four circuits and make measurements.)

Answer 1

We will analyse the current in each circuit one by one,

Circuit 1

\(V=\varepsilon-I R_{e f f}\)

\(9=10-I * 10\)

\(I=0.1 A\)

Circuit 2

\(V=\varepsilon-I R_{e f f}\)

\(9=10-I * 20\)

\(I=0.05 A\)

Circuit 3

\(V=\varepsilon-I R_{e f f}\)

The 2 resistors are in parallel,

10 ohm parallel with 10 ohm

effective resistance when two resistors are in parallel is given by,

\(R_{e f f}=\frac{R_{1} R_{2}}{R_{1}+R_{2}}\)

\(9=10-I * \frac{10 * 10}{10+10}\)

\(I=0.2 A\)

Circuit 4

\(V=\varepsilon-I R_{e f f}\)

The 3 resistors are in parallel,

10 ohm parallel with 10 ohm gives equivalent resistance of \(5 \mathrm{ohm}\), this 5 ohm is parallel with \(50 \mathrm{ohm}\)

effective resistance when two resistors are in parallel is given by,

\(R_{e f f}=\frac{R_{1} R_{2}}{R_{1}+R_{2}}\)

\(9=10-I * \frac{5 * 50}{50+5}\)

\(I=\frac{1}{4.55}=0.22 A\)

Therefore the descending order of total current coming from the battery,

Circuit \(4>\) Circuit \(3>\) Circuit \(1>\) Circuit 2