The sensitivity of a galvanometer of resistance 990ohm is increased by 10 times.The shunt used is??
990*R/(990+R) = 990/10.
990*R/(990+R) = 99.
990*R = (990+R)99.
10R = 990+R.
9R = 990.
R = 110 Ohms.
there is a small correction in the problem. the sensitivity does not increase but decreases.
the shunt is connected parallel to galvanometer. Imagine a circuit where main current is i and shunt is connected parallel to galvanometer. main current flowing is i into this combination. it is given that the sensitivity decreases by 10 times, the current flowing through the galvanometer become i / 10, the remaining current flows though the shunt that is 9 i/10. since shunt and galvanometer are in parallel the potential difference across both will be same, so
potential across galvanometer = potential across shunt
( using ohm's law)
(9 i/10) x s = (i / 10) x G
substitute the values given for G, so shunt s = 110 ohm.
Note: Since the current is 10 times the
previous current, the resistance is 1/10
of the previous resistance: 990/10.
To determine the shunt resistance used to increase the sensitivity of a galvanometer, you need to understand the concept of a shunt and its relationship with the resistance of the galvanometer.
A shunt is a low resistance connected in parallel with the galvanometer to divert some of the current and allow the measurement of larger currents without damaging the galvanometer or exceeding its range.
First, let's calculate the original current sensitivity of the galvanometer (Isens_gal).
Given:
Resistance of the galvanometer (R_gal) = 990 ohms
Since the sensitivity of a galvanometer is inversely proportional to its resistance, we can express it as:
Isens_gal = 1/R_gal
Substituting the given resistance value into the equation:
Isens_gal = 1/990
Now, we need to determine the increased sensitivity of the galvanometer, which is 10 times higher. Let's denote this as Isens_inc.
Isens_inc = 10 * Isens_gal
Substituting the value of Isens_gal:
Isens_inc = 10 * (1/990)
Next, we have to find the shunt resistance (R_shunt) that can produce the desired increased sensitivity. The shunt resistance can be calculated using the formula:
R_shunt = (R_gal * (1/Isens_inc)) - R_gal
Substituting the given values into the equation:
R_shunt = (990 * (1/Isens_inc)) - 990
R_shunt = (990 * (1/(10 * (1/990)))) - 990
Simplifying the expression:
R_shunt = (990 * (1/10) * (990/1)) - 990
R_shunt = (990 * (990/10)) - 990
After simplification, we get:
R_shunt = 9900 - 990
R_shunt = 8910 ohms
Therefore, the shunt used to increase the sensitivity of the galvanometer by 10 times is 8910 ohms.