A resistance of 200Ω is connected to a 120V supply. How much resistance must be connected in parallel with this to increase the current to 2A?
Understand the Problem
The question describes a circuit with a 200Ω resistor connected to a 120V supply. It asks to calculate the resistance that needs that has to be connected in parallel to increase the total current to 2A. We'll need to use Ohm's law to solve this problem.
Answer
The resistance that has to be connected in parallel is approximately $85.71Ω$.
Answer for screen readers
The resistance that must be connected in parallel is approximately $85.71Ω$.
Steps to Solve
- Calculate the current through the 200Ω resistor Use Ohm's law ($V = IR$) to find the current ($I_1$) through the 200Ω resistor:
$I_1 = \frac{V}{R_1} = \frac{120V}{200Ω} = 0.6A$
- Calculate the current through the parallel resistor Since the total current ($I_t$) is 2A, and we know the current through the first resistor ($I_1$) is 0.6A, we can find the current through the parallel resistor ($I_2$):
$I_2 = I_t - I_1 = 2A - 0.6A = 1.4A$
- Calculate the resistance of the parallel resistor Now we know $I_2$ and the voltage ($V$) across it (which is the same as the supply voltage, 120V, because it's in parallel). Use Ohm's law again to find the resistance ($R_2$) of the parallel resistor:
$R_2 = \frac{V}{I_2} = \frac{120V}{1.4A} \approx 85.71Ω$
The resistance that must be connected in parallel is approximately $85.71Ω$.
More Information
When resistors are connected in parallel, the voltage across each resistor is the same, and the total current is the sum of the currents through each resistor.
Tips
A common mistake is to calculate the total resistance of the parallel combination incorrectly or to forget that voltage is the same across parallel components. Another error is to assume that the 2A current flows only through the additional resistor.
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