what is the total resistance in a circuit having 3 feetof 10 ohm/ft wire, with two 15 ohm resistors wired in parallel?
if you mean 30 ohm in parallel with two 15 ohm resistors,
1/rt= 2/15 + 1/30= (4+1)/30
rt= 30/5
To determine the total resistance in this circuit, we need to consider the resistance contributed by each component. Let's break it down step by step:
1. Start with the length of wire: Given that there are 3 feet of wire with a resistance of 10 ohms per foot, we can calculate the total resistance of the wire by multiplying the resistance per foot (10 ohms/ft) by the length (3 ft). So, the resistance of the wire is 10 ohms/ft * 3 ft = 30 ohms.
2. Moving on to the resistors in parallel: When resistors are wired in parallel, the total resistance can be calculated using the formula:
1/RTotal = 1/R1 + 1/R2 + 1/R3 + ...
In your case, there are two 15-ohm resistors wired in parallel. So, applying the formula, we have:
1/RTotal = 1/15 ohms + 1/15 ohms = 2/15 ohms
To find RTotal, we need to take the reciprocal of this value:
RTotal = 15 ohms / 2 = 7.5 ohms
3. Finally, we can calculate the total resistance of the circuit by adding the resistances of the wire and the resistors. In this case, the total resistance is the sum of the wire resistance (30 ohms) and the combined resistance of the resistors (7.5 ohms):
Total Resistance = Wire Resistance + Resistor Resistance
= 30 ohms + 7.5 ohms
= 37.5 ohms
Therefore, the total resistance in the circuit is 37.5 ohms.