Video Transcript
What is the value of the multiplier
resistance required to convert a galvanometer that has a resistance of 0.2 ohms and
gives full-scale deflection when a current of two milliamps passes through it to a
voltmeter that measures potential difference up to 40 volts? (A) 20,000.2 ohms, (B)
19,999.8 ohms, (C) 5.00005 ohms, (D) 4.99995 ohms.
In this question, we’re considering
a galvanometer. And we need to find the multiplier
resistance needed to convert this galvanometer to a voltmeter that measures up to a
given potential difference. Let’s recall the equation that will
allow us to calculate the required multiplier resistance: 𝑅 M is equal to 𝑉 max
over 𝐼 G minus 𝑅 G, where 𝑅 M is the multiplier resistance. 𝑉 max is the maximum potential
difference we want to measure. 𝐼 G is the current that gives the
full-scale deflection on the galvanometer. And 𝑅 G is the resistance of the
galvanometer.
From the question, we can see that
𝐼 G is two milliamps, 𝑅 G𝐺 is 0.2 ohms, and 𝑉 max is 40 volts. We need to convert 𝐼 G into
amps. So we can recall that one milliamp
is 0.001 amps, and hence two milliamps is 0.002 amps. Since we know all the quantities on
the right-hand side of this equation, we can substitute them in to find the
multiplier resistance. 𝑅 M is equal to 40 volts divided
by 0.002 amps minus 0.2 ohms. Evaluating this expression, we find
𝑅 M to be 19,999.8 ohms. This corresponds to answer option
(B).
