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In parallel circuits, each component or branch has the same voltage across its terminals. This is one of the fundamental properties that distinguishes parallel circuits from series circuits. Because the voltage is constant in each branch, parallel circuits are very advantageous for distributing power to multiple devices from a single source.
It’s important to remember that while the voltage is constant in a parallel circuit, the current is not distributed equally. Instead, the total current flowing from the source is divided among the parallel branches. The amount of current that flows through each branch depends on the resistance of that branch. The lower the resistance, the higher the current that flows through it.

• Voltage is the same across all components in a parallel circuit.
• The total current is the sum of the currents through each parallel branch.

When solving problems involving parallel circuits, you can use Ohm’s Law, which states that the current (I) in a resistor is equal to the voltage (V) across the resistor divided by the resistance (R) of the resistor: \[ I = \frac{V}{R} \] This relationship allows us to calculate the current through each resistor, as we can see in the exercise discussed.

Resistor calculations in parallel circuits might initially seem complex, but they actually follow a straightforward pattern. In parallel configurations, the total or equivalent resistance can be calculated using the reciprocal formula. However, when given specific resistors and a fixed voltage, it becomes easier to individually calculate the current through each resistor.
Using Ohm's Law, once you know the voltage (or emf) across the entire parallel circuit, calculating the current flowing through each resistor becomes a matter of simple division:

Calculate the current through a resistor using
\[ I = \frac{V}{R} \]

If you have the current for one resistor and need to find the overall effect, remember that for any new resistor added in parallel, the total resistance of the circuit decreases, which subsequently increases the circuit’s total current.

• For a 20 kΩ resistor with a 2.5V drop, the current is 0.125 mA.
• For a 30 kΩ resistor with the same 2.5V drop, the current becomes 0.0833 mA.
• With a 75 kΩ resistor, it reduces further to 0.0333 mA.

Each resistor carries a different portion of the total current based on its resistance value.

Electromotive Force, or emf, is an essential component in circuitry. It is often described as the "pressure" that pushes electric current to flow through a circuit. In the scenario provided, the emf of the battery was determined using one branch of the parallel circuit, specifically the 20 kΩ resistor. By knowing the current in this branch, which was 0.125 mA, the voltage across it—or the emf—was determined to be 2.5 volts, showcasing Ohm's Law in action.
Though referred to as a "force," emf is actually a potential difference, measured in volts, not a force in the mechanical sense. It provides the energy per unit charge needed to drive the current through the resistance of the entire circuit without any inherent loss of energy.

• The emf is constant across all branches in a parallel circuit.
• It powers the circuit and maintains the voltage across resistors.

In practical terms, as shown, there's a universal application: once the emf is known, it can directly be used to compute other unknowns in the circuit, like the current through different resistors as we calculated for 30 kΩ and 75 kΩ resistors previously.