Series and parallel circuits

The current at every point in a series circuit is the same.

Therefore, the ammeter placed after R2 would also read 0.2A.

Answer: 0.2A

In a series circuit, there is only one path for the current to flow. The charge carriers (electrons) must pass through each component in turn. Since charge is conserved, the same number of charge carriers pass through each point in the circuit per unit time. Current is defined as the rate of flow of charge, therefore, the current must be the same at every point.

Current entering junction = Current leaving junction. Therefore, 3.0 A = 1.2 A + 0.8 A + I₃. Rearranging: I₃ = 3.0 A - 1.2 A - 0.8 A = 1.0 A. The current through the third resistor is 1.0 A.

This is due to the principle of conservation of charge. Electric charge (carried by electrons) cannot be created or destroyed. Therefore, the amount of charge flowing into a junction per unit time must equal the amount of charge flowing out of the junction per unit time. Since electric current is defined as the rate of flow of charge, the total current entering the junction must equal the total current leaving the junction.

Vtotal = V₁ + V₂ + V₃
12V = 2.5V + 4.5V + V₃
12V = 7V + V₃
V₃ = 12V - 7V
V₃ = 5V

In a series circuit, the total potential difference across all components must equal the source voltage.

The total potential difference (voltage) supplied by the power source represents the energy per unit charge available to the circuit. As charge flows through the series circuit, it expends energy as it passes through each component (resistor). The potential difference across each component represents the energy used by that component per unit charge. Because energy is conserved, the total energy used by all components must equal the total energy supplied by the source. Therefore, the sum of individual potential differences must equal the total potential difference of the power supply.

Answer:
The voltage across parallel resistors is the same.
Therefore, the voltage across the 12.0 Ω resistor is also 3.0 V.

Voltage = 3.0 V

Explanation: In a parallel circuit, potential difference is the same across each branch.

Answer:
In a parallel circuit, each resistor provides an alternative path for current to flow between the same two points in the circuit. These two points have a specific potential difference between them, dictated by the power supply and other circuit elements. Since each resistor is connected across these same two points, each resistor experiences the same potential difference. The current through each resistor will differ, depending on its resistance (V=IR), but the potential difference remains constant across all parallel branches.

1. Calculate the total resistance (R_total):
In a series circuit, R_total = R1 + R2 + R3
R_total = 2.0 Ω + 3.0 Ω + 1.0 Ω = 6.0 Ω

2. Calculate the current (I) using Ohm's Law:
V = IR, so I = V/R
I = 12.0 V / 6.0 Ω = 2.0 A

*Therefore, the current flowing through the circuit is 2.0 A. In a series circuit, the current is the same at all points.*

When identical lamps are added in parallel, the total resistance of the circuit decreases. Since the voltage of the battery remains constant, the total current drawn from the battery (I = V/R) increases significantly. A larger current means the battery is delivering energy at a faster rate, and therefore its energy is depleted more quickly. In a series circuit, adding lamps increases the total resistance, reducing the current and slowing the rate of energy depletion from the battery.

Total e.m.f. = sum of individual e.m.f.s
Total e.m.f. = 1.5 V + 1.5 V + 1.5 V + 1.5 V
Total e.m.f. = 6.0 V

Explanation: In a series circuit, the voltage of each cell adds up. Therefore, we add all the e.m.f. values together to get the total e.m.f. of the circuit.

When batteries are connected in series, the potential difference (voltage) across each battery adds up. This is because the batteries are connected end-to-end, forming a single path for the current. Each battery contributes to the overall potential difference, resulting in a higher total e.m.f. This higher e.m.f. provides more energy to each coulomb of charge flowing through the circuit.

Total resistance in a series circuit is the sum of the individual resistances.
Formula: R_total = R_1 + R_2
R_total = 3.0 Ω + 1.5 Ω = 4.5 Ω
Answer: 4.5 Ω

In a series circuit, the current has only one path to flow through. When a resistor is added in series, it introduces an additional obstacle to the flow of current. This additional opposition is quantified as resistance. Therefore, the total resistance is the sum of all individual resistances, so adding more resistors always increases the total resistance.

Answer:

* Formula: Total current (I_total) = I₁ + I₂ + I₃
* Working: I_total = 0.5 A + 1.2 A + 0.8 A = 2.5 A
* Answer: I_total = 2.5 A

Explanation: In a parallel circuit, the total current is the sum of the currents in each branch because the charge has multiple paths to flow through.

Answer:

In a parallel circuit, the current from the source splits into multiple paths (branches). Each branch provides an alternative route for the charge to flow. The source must supply enough current to satisfy the current demand in all the branches. Since each branch allows some charge to flow, the total current from the source is always the sum of the currents in each branch, and therefore larger than the current in any single branch.

Formula: 1/R = 1/R1 + 1/R2
Working: 1/R = 1/6.0 + 1/12.0 = 3/12.0
R = 12.0/3 = 4.0 Ω
Answer: 4.0 Ω
Explanation: The combined resistance of resistors in parallel is always less than the smallest individual resistance. This is because the parallel combination provides more paths for the current to flow.

When resistors are connected in parallel, the total current has more paths to flow through. This increased number of paths reduces the overall opposition to current flow, thus reducing the combined resistance. Adding another resistor in parallel is equivalent to widening a pipe to allow more water to flow.

1. If one lamp fails (burns out), the other lamps will continue to work. This is because each lamp has its own independent circuit.
2. Each lamp receives the full mains voltage (e.g. 230V), ensuring they all operate at their designed brightness.

In a parallel circuit, each lamp has the full mains voltage applied to it, resulting in optimal brightness for each lamp. Furthermore, if one lamp fails in a parallel circuit, the other lamps continue to function because they are on separate branches. In contrast, in a series circuit, the voltage is divided among the lamps, resulting in dimmer lights. If one lamp fails in a series circuit, the entire circuit is broken, and all lamps will switch off.

I = I₁ + I₂
I = 1.2 A + 0.8 A
I = 2.0 A

Explanation: The total current entering a junction is equal to the sum of the currents leaving the junction. This is due to the conservation of charge; charge cannot be created or destroyed, only transferred.

The sum of currents entering a junction is equal to the sum of the currents leaving the junction due to the principle of conservation of charge. Electric charge cannot be created or destroyed. Therefore, the amount of charge flowing into a junction per unit time (current in) must equal the amount of charge flowing out of the junction per unit time (current out). If this were not the case, charge would either accumulate or disappear at the junction, which is not possible.

Formula: 1/R_total = 1/R_1 + 1/R_2
Calculation: 1/R_total = 1/2.0 + 1/3.0 = 0.5 + 0.333 = 0.833
R_total = 1/0.833 = 1.2 Ω

Explanation: The total resistance of parallel resistors is always less than the smallest individual resistance. This is because the current has more paths to flow through.

When resistors are connected in parallel, the total current in the circuit has multiple paths to flow through. This is equivalent to increasing the cross-sectional area for the current to flow. A larger cross-sectional area reduces the overall opposition to current flow, therefore decreasing the total resistance of the circuit.