3 times
Assume that the increase in length is achieved by uniform reduction in the cross-sectional area of the wire. Then an increase in length by 4 times will result in the cross sectional area being reduced to a fifth of it original value. This will increase the resistance to five times its previous value.
Actually resistance is directly proportional to the length provided area remains constant. But as we stretch the wire only its volume would remain constant. So its area is to be decreased as length increases. V = pi r^2 * L Now we have R = K * L / pi r^2 Multiplying numerator and denominator by L we get R = K/V * L^2 So resistance is found to be proportional to square of length Hence as length gets increased by 2 times, its resistance value would increase by 4 times.
If both the diameter and length of a wire are quadrupled, the resistance of the wire will increase by a factor of 16. This is because resistance is directly proportional to the length of the wire and inversely proportional to the cross-sectional area of the wire, which is determined by the diameter. By quadrupling both, the resistance will increase by 4^2 = 16 times.
The new volume is 3^3 = 27 times as much.
The volume increases to 33 = 27 times as much.
When the length and width are tripled, the area becomes (3 x 3) = 9 times as much as before.
The word "tripled" means increased by three times.
Cell constant(C) = Resistance(R) X Specific Conductivity(K)
The heat released by the rheostat with double the voltage will quadruple. When voltage is tripled, the power loss is 32 or 9 times that before. A rheostat is a kind of variable resistor. Since E = IR (voltage equals current times resistance), then I = E/R (current equals voltage divided by resistance). If the voltage is doubled and the resistance stays the same, then--you can see by the formula--the current would double. Now, power dissipated by a resistor is related to the product of the current and voltage (P = IE). But since a doubling of voltage produces also a doubling of current, double the current results in 2X2=4 times the power (heat) loss.
Time period is directly proportional to the square root of the length So as we increase the length four times then period would increase by ./4 times ie 2 times.
just did this on castle learning the answer is six times
If displacement per unit time is tripled, velocity will increase by a factor of 3. This is because velocity is directly proportional to displacement per unit time in a linear relationship.