Correct Answer - Option 1 : kV/μs
The transient voltage appear across the contacts of circuit breaker at current zero period during arcing is known as Restriking voltage.
The expression for the re-striking voltage is \({V_C}\left( t \right) = {V_m}\left( {1 - \cos {ω _n}t} \right)\)
The maximum value of the re-striking voltage occurs at \(t = \frac{\pi }{{{ω _n}}} = \pi \sqrt {LC}\)
The maximum value of re-striking voltage = 2 Vm = 2 × peak value of the system voltage
The rate of rise of re-striking voltage (RRRV) \(= \frac{d}{{dt}}\left[ {{V_m}\left( {1 - \cos {ω _n}t} \right)} \right]\)
∴ RRRV = Vm ωn sin ωnt
The rate of rise of re-striking voltage is directly proportional to the natural frequency.
\(RRRV \propto {ω _n} \propto \frac{1}{{\sqrt {LC} }}\)
Where, L is the inductance of the system
C is the capacitance of the system
So, the rate of rise of re-striking voltage (RRRV) is dependent upon both the inductance and capacitance of the system.
Now, the maximum value of RRRV occurs when ωnt = π/2 i.e. when t = π/2ωn
∴The maximum value of RRRV \(= {V_m}{ω _n} = \frac{{{V_m}}}{{\sqrt {LC} }}\)
\(RRR{V_{max}} = \frac{{{V_m}}}{{\sqrt {LC} }}\)
RRRV is measured in kV / μ-sec
