Electricity - Series and Parallel Circuits

Calculate the total resistance and the total current for a circuit with a $12V$ battery connected to two resistors, $4\Omega$ and $8\Omega$, in series.

$R_{total} = 4\Omega + 8\Omega = 12\Omega$. Total current $I = \frac{V}{R_{total}} = \frac{12V}{12\Omega} = 1.0A$.

In a series circuit, resistors are simply added together. Using Ohm's Law $I = \frac{V}{R}$, we find the current flowing through the entire loop.

Two resistors, $R_1 = 10\Omega$ and $R_2 = 10\Omega$, are connected in parallel to a $5V$ power supply. Determine the equivalent resistance $R_p$ and the current through $R_1$.

$\frac{1}{R_p} = \frac{1}{10\Omega} + \frac{1}{10\Omega} = \frac{2}{10\Omega} \Rightarrow R_p = 5\Omega$. Current through $R_1$: $I_1 = \frac{V}{R_1} = \frac{5V}{10\Omega} = 0.5A$.

For parallel circuits, the reciprocal sum is used for resistance. The voltage across each resistor is the same as the source ($5V$), allowing us to calculate individual branch currents using Ohm's Law.

A circuit consists of a $24V$ DC supply and three resistors $R_1 = 2\Omega$, $R_2 = 4\Omega$, and $R_3 = 6\Omega$ connected in series. Calculate the potential difference across the $4\Omega$ resistor ($V_2$).

1. Calculate total resistance ($R_s$): $R_s = R_1 + R_2 + R_3$ $R_s = 2\Omega + 4\Omega + 6\Omega = 12\Omega$
2. Calculate total current ($I$): $I = \frac{V}{R_s}$ $I = \frac{24V}{12\Omega} = 2A$
3. Calculate voltage across $R_2$: $V_2 = I \times R_2$ $V_2 = 2A \times 4\Omega = 8V$

In a series circuit, current is uniform. By finding the total resistance first, we determine the current flowing through every component, then apply Ohm's Law specifically to the resistor in question.

A $12V$ battery is connected to two resistors in parallel: $R_1 = 6\Omega$ and $R_2 = 12\Omega$. Calculate the total current ($I_{total}$) supplied by the battery.

1. Calculate equivalent resistance ($R_p$): $\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2}$ $\frac{1}{R_p} = \frac{1}{6} + \frac{1}{12} = \frac{2}{12} + \frac{1}{12} = \frac{3}{12}$ $R_p = \frac{12}{3} = 4\Omega$
2. Calculate total current ($I_{total}$): $I_{total} = \frac{V}{R_p}$ $I_{total} = \frac{12V}{4\Omega} = 3A$

For parallel circuits, we find the reciprocal of the total resistance by summing the reciprocals of individual resistances. Once the equivalent resistance is known, Ohm's Law provides the total current.