Finding Current in a Parallel Circuit

Finding Current in a Parallel Circuit

In parallel circuit, the potential difference (V) across each of the resistors is equal to the e.m.f. (E) if the internal resistance of the cell is ignored.

By Ohm’s Law
$$\begin{array}{l}{I}_1=\frac{E}{R_1}\\ I_2=\frac{E}{R_2}\end{array}$$

Example 1:

For the diagram above,
a. find the reading of the ammeter.
b. find the current in each of the resistors.

Answer:
a.
Effective resistance of the 2 resistors in parallel
$$R={\left(\frac{1}{6}+\frac{1}{3}\right)}^{-1}=2\Omega$$ Potential difference across the 2 resistance, V = 3V
$$\begin{array}{l}V=IR\\ (3)=I(2)\\ I=\frac{3}{2}=\mathrm{1.5A}\end{array}$$
Reading of the ammeter = 1.5A
b.
Current in the 3Ω resistor,
$$\begin{array}{l}V=IR\\ (3)=I(3)\\ I=1.0A\end{array}$$ Current in the 6Ω resistor,
$$\begin{array}{l}V=IR\\ (3)=I(6)\\ I=0.5A\end{array}$$

Example 2

Figure above shows 3 identical resistors connected in parallel in a circuit. Given that the resistance of the resistors are 6Ω each. Find the reading of all the ammeters in the figure above.
Answer:
The potential diffrence across the resistors V = 6V
For ammeter A,
The equivalent resistance = 6/3 = 2Ω.
$$\begin{array}{l}V=IR\\ (6)=I(2)\\ I=3A\end{array}$$
For ammeter A1,
$$\begin{array}{l}V=IR\\ (6)=I(6)\\ I=1A\end{array}$$ For ammeter A2,
$$\begin{array}{l}V=IR\\ (6)=I(6)\\ I=1A\end{array}$$