Distinguish between resistance and resistivity - Leaving Cert Physics - Question 8 - 2017

The resistance decreases. When the diameter of the wire is increased by a factor of three, the cross-sectional area increases by a factor of nine (since area is proportional to the square of the diameter). Resistance is inversely proportional to the cross-sectional area, which means the resistance will decrease by a factor of nine.

RMS stands for root mean square. It is a statistical measure of the magnitude of a varying quantity and is especially useful in electrical engineering to describe the effective value of an alternating current (a.c.), which is the average voltage or current over one complete cycle.

A.C. stands for alternating current, which is an electric current that periodically reverses direction, in contrast to direct current (D.C.) which flows in one direction only.

To find the effective resistance (R_p) of the circuit, we can use the formula:

$\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2}$

Here, R_1 = 200 Ω and R_2 = 500 Ω. Plugging the values in:

$\frac{1}{R_p} = \frac{1}{200} + \frac{1}{500} = \frac{2.5 + 1}{500} = \frac{3.5}{500}$

Simplifying gives:

$R_p = \frac{500}{3.5} \approx 143 \ \, \Omega$

Using Ohm's law to find the current (I) flowing through the 200 Ω resistor, we can apply:

$I = \frac{V}{R}$

Where V = 12 V (the rms voltage applied) and R = 200 Ω.

Thus:

$I_{200} = \frac{12}{200} = 0.06 A$

When the variable resistor is removed, the total resistance in the circuit decreases; hence, the overall current supplied by the voltage source will increase according to Ohm’s Law. This increase in total current will lead to a higher current flowing through the 50 Ω resistor, specifically increasing as it's directly influenced by the reduction in overall resistance.

When the 50 Ω resistor is replaced with a coil of the same resistance, the current flowing will typically reduce due to the inductive reactance of the coil in an a.c. circuit. This inductance causes an opposition to the change in current, reducing the effective current further.

Replacing the 50 Ω resistor with a diode will cause the current to flow in one direction only due to the nature of diodes. In a.c., the diode only allows current to pass during one half of the cycle, effectively limiting the current, resulting in a lower total current flowing through the circuit.