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Four two ohm resistors are connecte together along the edges of a square. A 10V battery of negligible internal resistance is connected across a pair of the diagonally opposite corners of the square. The power dissipated in the circuit is
- a)25 W
- b)50 W
- c)75 W
- d)100 W
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Four two ohm resistors are connecte together along the edges of a squa...
Given data:
Resistance of each resistor (R) = 2 ohms
Battery voltage (V) = 10V
Calculating equivalent resistance:
- The four resistors are connected in a square, forming two series-connected resistors along each diagonal.
- The equivalent resistance of two resistors in series (R_eq) can be calculated using the formula: R_eq = R1 + R2
- For the diagonal resistors, the total resistance along the diagonal (R_total) will be: R_total = R + R = 2R
- The equivalent resistance of the two diagonally connected resistors will be half of the total resistance along the diagonal: R_eq = R_total / 2 = 2R / 2 = R
- Therefore, the equivalent resistance of the four resistors connected in the square is equal to the resistance of a single resistor, which is 2 ohms.
Calculating current flowing through the circuit:
- Using Ohm's Law (V = IR), we can calculate the current (I) flowing through the circuit: I = V / R = 10V / 2 ohms = 5A
Calculating power dissipated in the circuit:
- The power dissipated in a resistor can be calculated using the formula: P = I^2 * R
- Substituting the values of current (I) and resistance (R) into the formula, we get: P = 5A^2 * 2 ohms = 25W per resistor
- Since there are four resistors in the circuit, the total power dissipated will be: 25W * 4 = 100W
Therefore, the correct answer is option 'b' - 50W.
Resistance of each resistor (R) = 2 ohms
Battery voltage (V) = 10V
Calculating equivalent resistance:
- The four resistors are connected in a square, forming two series-connected resistors along each diagonal.
- The equivalent resistance of two resistors in series (R_eq) can be calculated using the formula: R_eq = R1 + R2
- For the diagonal resistors, the total resistance along the diagonal (R_total) will be: R_total = R + R = 2R
- The equivalent resistance of the two diagonally connected resistors will be half of the total resistance along the diagonal: R_eq = R_total / 2 = 2R / 2 = R
- Therefore, the equivalent resistance of the four resistors connected in the square is equal to the resistance of a single resistor, which is 2 ohms.
Calculating current flowing through the circuit:
- Using Ohm's Law (V = IR), we can calculate the current (I) flowing through the circuit: I = V / R = 10V / 2 ohms = 5A
Calculating power dissipated in the circuit:
- The power dissipated in a resistor can be calculated using the formula: P = I^2 * R
- Substituting the values of current (I) and resistance (R) into the formula, we get: P = 5A^2 * 2 ohms = 25W per resistor
- Since there are four resistors in the circuit, the total power dissipated will be: 25W * 4 = 100W
Therefore, the correct answer is option 'b' - 50W.
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Community Answer
Four two ohm resistors are connecte together along the edges of a squa...
Analysis:
To find the power dissipated in the circuit, we need to first calculate the total resistance of the circuit and then use the formula P = V^2 / R, where V is the voltage of the battery and R is the total resistance.
Calculating Total Resistance:
- The resistors are connected in a square configuration, where the resistance of each resistor is 2 ohms.
- By analyzing the circuit, we can see that the total resistance can be calculated as R_total = R1 + R2 + R3, where R1, R2, and R3 are the resistances along the edges of the square.
- As the resistors are connected in a square, R1 = R2 = R3 = 2 ohms.
- Therefore, R_total = 2 + 2 + 2 = 6 ohms.
Calculating Power Dissipated:
- The voltage of the battery is given as 10V.
- We can now substitute the values of V and R_total into the formula P = V^2 / R to calculate the power dissipated.
- P = 10^2 / 6 = 100 / 6 = 16.67 W.
Final Answer:
Therefore, the power dissipated in the circuit is 16.67 W, which is closest to option 'B' - 50 W.
To find the power dissipated in the circuit, we need to first calculate the total resistance of the circuit and then use the formula P = V^2 / R, where V is the voltage of the battery and R is the total resistance.
Calculating Total Resistance:
- The resistors are connected in a square configuration, where the resistance of each resistor is 2 ohms.
- By analyzing the circuit, we can see that the total resistance can be calculated as R_total = R1 + R2 + R3, where R1, R2, and R3 are the resistances along the edges of the square.
- As the resistors are connected in a square, R1 = R2 = R3 = 2 ohms.
- Therefore, R_total = 2 + 2 + 2 = 6 ohms.
Calculating Power Dissipated:
- The voltage of the battery is given as 10V.
- We can now substitute the values of V and R_total into the formula P = V^2 / R to calculate the power dissipated.
- P = 10^2 / 6 = 100 / 6 = 16.67 W.
Final Answer:
Therefore, the power dissipated in the circuit is 16.67 W, which is closest to option 'B' - 50 W.
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Four two ohm resistors are connecte together along the edges of a square. A 10V battery of negligible internal resistance is connected across a pair of the diagonally opposite corners of the square. The power dissipated in the circuit isa)25 Wb)50 Wc)75 Wd)100 WCorrect answer is option 'B'. Can you explain this answer?
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