Solving Electric Circuits

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Questions and Answers

In a circuit with resistors in parallel, what remains the same across each resistor?

  • Current
  • Resistance
  • Voltage (correct)
  • Power

If two resistors of equal value are connected in parallel, how does the equivalent resistance relate to the individual resistance?

  • It is twice the value of one resistor.
  • It is equal to the value of one resistor.
  • It is one-fourth the value of one resistor.
  • It is half the value of one resistor. (correct)

In a series circuit, how is the total resistance calculated?

  • By taking the square root of the sum of each resistance.
  • By summing the reciprocals of each resistance.
  • By summing the values of each resistance. (correct)
  • By averaging the values of all resistors.

What is the primary purpose of calculating equivalent resistance in a circuit?

<p>To simplify the circuit for easier analysis. (A)</p> Signup and view all the answers

When calculating the total resistance of a parallel and series combination, which part should be solved first?

<p>The parallel combination first. (B)</p> Signup and view all the answers

What happens to the total current in a circuit when additional resistors are added in parallel?

<p>The total current increases. (A)</p> Signup and view all the answers

How does the voltage drop across a resistor in a series circuit relate to its resistance value compared to other resistors in the series?

<p>Higher resistance, higher voltage drop. (B)</p> Signup and view all the answers

If a 10-ohm resistor and a 20-ohm resistor are connected in series to a 90V source, what is the current flowing through the 10-ohm resistor?

<p>3 Amperes (B)</p> Signup and view all the answers

Resistors $R_1$ and $R_2$ are connected in parallel. If $R_1 = 6\Omega$ and the total resistance of the parallel combination is $3\Omega$, what is the value of $R_2$?

<p>6 Ω (B)</p> Signup and view all the answers

A circuit has a total resistance of $15\Omega$ and is powered by a 60V source. What is the total current flowing through the circuit?

<p>4A (C)</p> Signup and view all the answers

In a series-parallel circuit, a parallel branch consists of two $8\Omega$ resistors. What is the equivalent resistance of this branch?

<p>4 Ω (D)</p> Signup and view all the answers

A series circuit has a $6\Omega$ resistor and a $7\Omega$ resistor. If the current through the $6\Omega$ resistor is 4A, what is the voltage drop across the $7\Omega$ resistor?

<p>28V (D)</p> Signup and view all the answers

If the voltage across a parallel branch is 8V and one of the resistors in the branch is $4\Omega$, what is the current through that resistor?

<p>2A (D)</p> Signup and view all the answers

The total current entering a parallel combination of two resistors is 4A. If the current through one resistor is 2A, what is the current through the other resistor?

<p>2A (C)</p> Signup and view all the answers

Suppose you have two parallel resistors with $R_1 = 4\Omega$ and $R_2 = 4\Omega$ connected in series with $R_3 = 6\Omega$ and $R_4 = 7\Omega$. What is the voltage drop across the combination of $R_3$ and $R_4$ if the total current is 4A?

<p>52V (B)</p> Signup and view all the answers

Two resistors, $R_1 = 4\Omega$ and $R_2 = 4\Omega$, are connected in parallel. What is the equivalent resistance of this parallel combination?

<p>2 Ω (B)</p> Signup and view all the answers

A circuit consists of a parallel combination of two resistors ($R_1$ and $R_2$) in series with two other resistors ($R_3$ and $R_4$). If the total voltage is 60V and the voltage across the parallel combination is 8V, what is the voltage across the series combination of $R_3$ and $R_4$?

<p>52V (B)</p> Signup and view all the answers

If two resistors ($R_3$ and $R_4$) in series have a combined voltage drop of 52V and a current of 4A, what is their combined resistance?

<p>13 Ω (B)</p> Signup and view all the answers

Resistors $R_1$ and $R_2$ are in parallel, with $R_1 = 4\Omega$ and a voltage $U_{R1} = 8V$. What is the current through $R_1$?

<p>2A (D)</p> Signup and view all the answers

In a circuit where a parallel branch ($R_1$ and $R_2$) is in series with resistors $R_3$ and $R_4$, if the total current is 4A, what is the current through the series combination of $R_3$ and $R_4$?

<p>4A (D)</p> Signup and view all the answers

Flashcards

Equivalent Resistance

The total opposition to current flow in a circuit.

Parallel Combination

Resistors connected side-by-side, providing multiple paths for current.

Series Combination

Resistors connected end-to-end, forming a single path for current.

Ohm's Law Formula

Ohm's Law states that voltage equals current times resistance.

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Voltage Drop

The potential difference across a component.

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Voltage in Parallel

The voltage is the same across parallel components.

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Total Circuit Resistance

Total Resistance (Rc) = 15Ω

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Total Circuit Voltage

Total Voltage (U) = 60V

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Voltage across R3 and R4

Voltage across R3 + R4 = 52V

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Voltage across R1 and R2

Voltage across R1 and R2 = 8V

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Current through R1

Current through R1 = 2A

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Current through R2

Current through R2 = 2A

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Current through R3 and R4

Current through R3 + R4 = 4A

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Study Notes

  • To solve an electric circuit, begin by identifying all given values, such as current and resistance.

Equivalent Resistance Calculation

  • First calculate the equivalent resistance of the circuit
  • For resistors in parallel, like and , the equivalent resistance () is calculated using:
  • For and : = ((4)(4))/(4 + 4) = 16/8 = 2Ω
  • For resistors in series, like and the equivalent resistance is the sum of individual resistances.
  • If is in series with and then: = + + = 2 + 6 + 7 = 15Ω

Voltage Calculation

  • Apply Ohm's Law (U = I x ) to find the voltage.
  • If the Current is 4A and = 15Ω, then: U = 4 x 15 = 60V

Voltage Drops

  • Calculate voltage drops across different parts of the circuit to determine the distribution of voltage.
  • For resistors and , calculate: = I x (+ ) = 4 x (6 + 7) = 4 x 13 = 52V
  • Calculate the voltage across the parallel branch: = U - = 60 - 52 = 8V
  • In a parallel circuit, resistors and have the same voltage: = = 8V

Current

  • Use Ohm's Law (I = U/R) to find the current through and :
  • = / = 8/4 = 2A
  • = / = 8/4 = 2A
  • The current through and is the same as the total current:
  • = I = 4A

Final Answers

  • Total Resistance () = 15Ω
  • Total Voltage (U) = 60V
  • Voltage across () = 52V
  • Voltage across and () = 8V
  • Current through () = 2A
  • Current through () = 2A
  • Current through () = 4A

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