Two resistors are connected in parallel and connected to a voltage source of 12 V. The resistance of the first resistor is 24 ohms.

| January 3, 2021 | education

Two resistors are connected in parallel and connected to a voltage source of 12 V. The resistance of the first resistor is 24 ohms. Determine the resistance of the second resistor if the total current in the circuit is 0.75 A.

U = 12V.
R1 = 24 ohms.
I = 0.75 A.
R2 -?
When resistors are connected in parallel, their total resistance R is determined by the formula: R = R1 * R2 / (R1 + R2).
The total voltage U and the voltage across the resistors U1 and U2 are the same when connected in parallel: U = U1 = U2.
The current I with parallel connection will be the sum: I = I1 + I2.
According to Ohm’s law for a section of the circuit, we find the current in the first resistor I1: I1 = U1 / R1 = U / R1.
I1 = 12V / 24 Ohm = 0.5 A.
The current strength in the second resistor I2 is found by the formula: I2 = I – I1.
I2 = 0.75 A – 0.5 A = 0.25 A.
R2 = U2 / I2 = U / I2.
R2 = 12V / 0.25A = 48 Ohm.
Answer: the resistance of the second resistor is R2 = 48 ohms.



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