Base your answers to questions 63 through 66 on the circuit...

Base your answers to questions 63 through 66 on the circuit diagram below. The reading of ammeter $A_{1}$ is $2.0$ amperes. Neglect the resistance of the connecting wires and the battery. The potential difference supplied by battery $B$ is (A) $1.0 \mathrm{~V}$ (B) $2.0 \mathrm{~V}$ (C) $6.0 \mathrm{~V}$ (D) $12 \mathrm{~V}$

Base your answers to questions 63 through 66 on the circuit diagram below. The reading of ammeter $A_{1}$ is $2.0$ amperes. Neglect the resistance of the connecting wires and the battery.
The potential difference supplied by battery $B$ is
(A) $1.0 \mathrm{~V}$
(B) $2.0 \mathrm{~V}$
(C) $6.0 \mathrm{~V}$
(D) $12 \mathrm{~V}$

Key Concepts

Series and Parallel Circuits

Understanding series and parallel circuits is key in circuit analysis. In series circuits, components share the same current but the voltage divides among them according to their resistances, while in parallel circuits, all components have the same voltage across them but the current divides inversely proportional to their resistances. This differentiation is critical when determining overall current and voltage distribution in a circuit.

Ohm's Law

Ohm's Law is a fundamental principle in electrical circuits which states that the voltage across a resistor is directly proportional to the current flowing through it, with the proportionality constant being the resistance (V = IR). This relationship is essential for calculating unknown quantities when two of the three variables—voltage, current, and resistance—are known.

Kirchhoff's Circuit Laws

Kirchhoff's Circuit Laws, including the Voltage Law (KVL) and Current Law (KCL), are used to analyze complex circuits. KVL states that the sum of the electrical potential differences around any closed network is zero, ensuring that the energy is conserved in a loop. KCL states that the total current entering a junction equals the total current leaving it, a principle crucial for understanding current distribution in circuits.

Ideal Circuit Assumptions

Ideal circuit assumptions involve neglecting the resistance of connecting wires and assuming batteries have no internal resistance. These simplifications allow for a focus on the fundamental relationships between voltage, current, and resistance without the complexities introduced by non-ideal components, which in turn helps in understanding the basic behavior of electrical circuits.

Transcript

00:02 Referring to the electric circuit diagram in the left side of the screen, we are given that the amateur a1 here reads two amps, and we are to neglect the resistance of the connecting wires and the internal resistance of the battery.

00:19 The question is, what is the potential difference across battery b? four options are given to us.

00:26 So let's agree that we consider conventional current so that we know that there's a total current going in clockwise direction.

00:39 So that's coming out from the positive terminal of our battery b here.

00:43 And it flows through this connecting wire.

00:48 And at this junction here, let's call this junction a, the total current will break into two pathways.

00:55 So some will go to this branch and that will be the current through two and the current through resistor three.

01:04 And some, of course, will go through the middle branch.

01:09 And this would be the current through resistor one, which is, of course, the same current that flows through amateur one.

01:17 And that gives amateur one the reading of two amps.

01:20 Therefore, we can see that the branch current here in the middle branch is two amps.

01:25 So for us to determine the voltage across the battery here, we just need to take note that since the total current here has been distributed to two branches here at junction a, then we know that this middle branch here is parallel to the right...

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