15 Aug, 2024
· Physics · Technology

Compare the two circuit diagrams in question

If one of the resistors is turned off (a light bulb goes out), what happens to the other resistors (light bulbs) in both situations?

  • In both cases: All of the other bulbs go out as well.
  • In both cases: All of the other bulbs will stay lit and be brighter.
  • In the series circuit: All of the other bulbs will go out.
  • In parallel: The rest remain lit.
  • In the series circuit: The remaining bulbs stay lit and get brighter.
  • In parallel: They all go out.
Short Answer
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Long Explanation

Explanation

Series Circuit

In a series circuit, all components are connected end-to-end in a single path for the current to flow.

Impact of One Resistor (Bulb) Turning Off

When one resistor or light bulb in a series circuit is turned off, the entire circuit is broken. This means:

  • All other light bulbs will go out.
  • The current flow is interrupted, so no electricity reaches the remaining bulbs.

Parallel Circuit

In a parallel circuit, components are connected across multiple paths, so the current has more than one route to take.

Impact of One Resistor (Bulb) Turning Off

When one resistor or light bulb in a parallel circuit is turned off:

  • The other bulbs remain lit.
  • The current can still flow through the other paths.

Brightness of Remaining Bulbs

In parallel circuits, when one bulb goes out, the brightness of the remaining bulbs stays the same because each branch in a parallel circuit operates independently.

Important Equations

For a series circuit with resistors R1,R2,…,RnR_1, R_2, \ldots, R_n:

Rtotal=R1+R2+⋯+RnR_{\text{total}} = R_1 + R_2 + \cdots + R_n

For a parallel circuit with resistors R1,R2,…,RnR_1, R_2, \ldots, R_n:

1Rtotal=1R1+1R2+⋯+1Rn\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \cdots + \frac{1}{R_n}

These formulas illustrate how the total resistance differs between series and parallel circuits, affecting current flow and brightness of the bulbs accordingly.

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Concept

Series Circuit

Understanding Series Circuit

A series circuit is an electrical circuit in which components are connected end-to-end so that the current flows through each component without branching off. This means that there is only one path for the electrons to take. If one component fails, the entire circuit is interrupted.

Characteristics

  • Single Pathway: Since all components are connected in a row, there is only one path for current to travel.
  • Same Current: The current II is the same through all components.
  • Voltage Division: The total voltage VV of the power source is divided among the components.

Calculating Total Resistance

The total resistance RtotalR_{total} in a series circuit is the sum of the individual resistances R1,R2,…,RnR_1, R_2, \ldots, R_n:

Rtotal=R1+R2+…+RnR_{total} = R_1 + R_2 + \ldots + R_n

Voltage Drop

The voltage drop across each resistor can be calculated using Ohm's Law V=IRV = IR. The sum of the voltage drops across all components equals the total voltage of the power source:

Vtotal=V1+V2+…+VnV_{total} = V_1 + V_2 + \ldots + V_n

Here,

Vn=I⋅RnV_n = I \cdot R_n

Example

Assume you have a series circuit with three resistors:

R1=2 Ω,R2=3 Ω,R3=5 ΩR_1 = 2 \, \Omega, \quad R_2 = 3 \, \Omega, \quad R_3 = 5 \, \Omega

Connected to a 10V battery. The total resistance is:

Rtotal=R1+R2+R3=2+3+5=10 ΩR_{total} = R_1 + R_2 + R_3 = 2 + 3 + 5 = 10 \, \Omega

Since the current is the same throughout, you can find the current II using:

I=VtotalRtotal=10V10 Ω=1 AI = \frac{V_{total}}{R_{total}} = \frac{10V}{10 \, \Omega} = 1 \, A

The voltage drop across each resistor would be:

V1=I⋅R1=1 A⋅2 Ω=2VV_1 = I \cdot R_1 = 1 \, A \cdot 2 \, \Omega = 2V V2=I⋅R2=1 A⋅3 Ω=3VV_2 = I \cdot R_2 = 1 \, A \cdot 3 \, \Omega = 3V V3=I⋅R3=1 A⋅5 Ω=5VV_3 = I \cdot R_3 = 1 \, A \cdot 5 \, \Omega = 5V

Practical Considerations

In real-life applications, series circuits are used in devices where you want components to share the same current. However, one drawback is that if one component fails, the entire circuit stops working. Moreover, components like resistors in a series circuit will experience varying amounts of voltage drop.

Understanding these basics allows for better design and troubleshooting of electrical circuits!

Concept

Parallel Circuit

Basic Concepts of a Parallel Circuit

A parallel circuit is a type of electrical circuit in which multiple components are connected across the same set of electrically common points, creating multiple paths for current to flow. In a parallel configuration, each component is connected to the same voltage source.

Current in a Parallel Circuit

In a parallel circuit, the total current is the sum of the currents through each individual component. This can be mathematically represented as:

Itotal=I1+I2+I3+⋯+InI_{total} = I_1 + I_2 + I_3 + \cdots + I_n

where ItotalI_{total} is the total current and I1,I2,I3,…,InI_1, I_2, I_3, \ldots, I_n are the currents through each component.

Voltage in a Parallel Circuit

In this type of circuit, the voltage across each component is the same and is equal to the voltage of the power source:

Vtotal=V1=V2=V3=⋯=VnV_{total} = V_1 = V_2 = V_3 = \cdots = V_n

Resistance in a Parallel Circuit

Calculating the total resistance in a parallel circuit differs from that in a series circuit. The reciprocal of the total resistance (RtotalR_{total}) is the sum of the reciprocals of each individual resistance (RiR_i):

1Rtotal=1R1+1R2+1R3+⋯+1Rn\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \cdots + \frac{1}{R_n}

Therefore, the total resistance is:

Rtotal=(1R1+1R2+1R3+⋯+1Rn)−1R_{total} = \left( \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \cdots + \frac{1}{R_n} \right)^{-1}

Key Characteristics

  • Constant Voltage: Each component in a parallel circuit experiences the same voltage.
  • Variable Currents: The current through each component can differ depending on its resistance.
  • Lower Total Resistance: The overall resistance of the circuit is reduced with each additional parallel component.

By understanding these basic concepts, one can effectively analyze and design parallel circuits for various electrical and electronic applications.